Determining responses of rapidly varying mimo-ofdm communication channels using observation scalars

ABSTRACT

In an embodiment, a channel estimator includes first, second, and third stages. The first stage is configurable to generate a first observation scalar for a first communication path of a first communication channel, and the second stage is configurable to generate a second observation scalar for a first communication path of a second communication channel. And the third stage is configurable to generate channel-estimation coefficients in response to the first and second observation scalars. For example, such a channel estimator may use a recursive algorithm, such as a Vector State Scalar Observation (VSSO) Kalman algorithm, to estimate the responses of channels over which propagate simultaneous orthogonal-frequency-division-multiplexed (OFDM) signals (e.g., MIMO-OFDM signals) that suffer from inter-carrier interference (ICI) due to Doppler spread. Such a channel estimator may estimate the channel responses more accurately, more efficiently, with a less-complex algorithm, and with less-complex software or circuitry, than conventional channel estimators.

PRIORITY CLAIM

The present application claims the benefit of priority to the followingapplications, and is a Continuation-in-Part of copending U.S. patentapplication Ser. No. 12/963,569, filed Dec. 8, 2010, which applicationclaims the benefit of U.S. Provisional Patent Application Nos.61/267,667, filed Dec. 8, 2009, now expired, and 61/360,367, filed Jun.30, 2010, now expired, and which application is a Continuation-in-Partof copending U.S. patent application Ser. Nos. 12/579,935, filed Oct.15, 2009, and 12/579,969, filed Oct. 15, 2009, which applications claimthe benefit of U.S. Provisional Patent Application Serial Nos.61/105,704, filed Oct. 15, 2008, now expired, and 61/158,290, filed Mar.6, 2009, now expired; the present application also claims the benefit ofcopending U.S. Provisional Patent Application Ser. No. 61/495,218, filedJun. 9, 2011; all of the foregoing applications are incorporated hereinby reference in their entireties.

RELATED APPLICATION DATA

The present application is related to copending U.S. patent applicationSer. No. 13/284,890, entitled “PILOT PATTERN FOR OBSERVATION-SCALARMIMO-OFDM”, filed Oct. 29, 2011; U.S. patent application Ser. No.13/284,894, entitled “DETERMINING A RESPONSE OF A RAPIDLY VARYING OFDMCOMMUNICATION CHANNEL USING AN OBSERVATION SCALAR”, filed Oct. 29, 2011;and U.S. patent application Ser. No. 13/284,898, entitled “PILOT PATTERNFOR MIMO-OFDM”, filed Oct. 29, 2011; all of the foregoing applicationsare incorporated herein by reference in their entireties.

SUMMARY

In an embodiment, a channel estimator includes first, second, and thirdstages. The first stage is configurable to generate a first observationscalar for a first communication path of a first communication channel,and the second stage is configurable to generate a second observationscalar for a first communication path of a second communication channel.And the third stage is configurable to generate channel-estimationcoefficients in response to the first and second observation scalars.

For example, such a channel estimator may use a recursive algorithm,such as a Vector State Scalar Observation (VSSO) Kalman algorithm, toestimate the responses of channels over which propagate simultaneousorthogonal-frequency-division-multiplexed (OFDM) signals (e.g.,MIMO-OFDM signals) that suffer from inter-carrier interference (ICI) dueto Doppler spread. Such a channel estimator may estimate the channelresponses more accurately, more efficiently, with a less-complexalgorithm (e.g., with an algorithm that does not require a real-timematrix inversion), and with less-complex software or circuitry, thanconventional channel estimators. Furthermore, such a channel estimatormay be able to dynamically account for changes in the number ofcommunication paths that compose each channel, for changes in the delaysof these paths, and for changes in the signal-energy levels of thesepaths.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an embodiment of base and clientorthogonal-frequency-division-multiplexing (OFDM) transmitter-receiversthat are not moving significantly relative to one another while they arecommunicating with one another.

FIG. 2 is a plot of an embodiment of the frequencies of the carriersignals (solid lines) generated by the presently transmittingtransmitter-receiver of FIG. 1, and of the frequency “slots” (dashedlines) that these carrier signals may respectively occupy at thepresently receiving transmitter-receiver of FIG. 1.

FIG. 3 is a block diagram of an embodiment of base and client OFDMtransmitter-receivers that are moving relative to one another while theyare communicating with one another.

FIG. 4 is a plot of an embodiment of the frequencies of carrier signals(solid lines) generated by the presently transmittingtransmitter-receiver of FIG. 3, and of the frequency slot (dashed line)that the center one of these plotted carrier signals may occupy at thepresently receiving transmitter-receiver of FIG. 3.

FIG. 5 is a plot of an embodiment of the frequencies of carrier signalsgenerated by the presently transmitting transmitter-receiver of FIG. 3,where the carrier signals are grouped into clusters of data carriersignals (data clusters) and clusters of pilot carrier signals (pilotclusters).

FIG. 6 is a plot of an embodiment of data clusters and pilot clustersgenerated by the presently transmitting transmitter-receiver of FIG. 3,where the pilot clusters have a uniform separation.

FIG. 7 is a plot of an embodiment of a pilot cluster.

FIG. 8 is a plot of another embodiment of a pilot cluster.

FIG. 9 is a block diagram of an embodiment of the receiver of one orboth of the base and client transmitter-receivers of FIG. 3.

FIG. 10 is a block diagram of an embodiment of the channel estimator ofFIG. 9.

FIG. 11 is a diagram of an embodiment of base and client MIMO-OFDMtransmitter-receivers that are moving relative to one another while theyare communicating with one another, and of the communication pathsbetween multiple base transmit antennas and a single client receiveantenna.

FIG. 12 is a diagram of an embodiment of base and client MIMO-OFDMtransmitter-receivers that are moving relative to one another while theyare communicating with one another, and of the communication pathsbetween multiple base transmit antennas and multiple client receiveantennas.

FIG. 13 is a block diagram of an embodiment of the receiver of one orboth of the base and client transmitter-receivers of FIGS. 11 and 12.

FIG. 14 is a block diagram of an embodiment of a portion of the channelestimator of FIG. 13, the portion associated with a single receiveantenna.

FIG. 15 is a block diagram of an embodiment of apartial-channel-estimation-matrix combiner of the channel estimator ofFIG. 13.

FIG. 16 is a block diagram of an embodiment of the received-signalcombiner of FIG. 13.

FIG. 17 is a block diagram of an embodiment of a transmitter of one orboth of the base and client transmitter-receivers of FIGS. 11 and 12.

DETAILED DESCRIPTION

FIG. 1 is a block diagram of an embodiment of a basetransmitter-receiver 10 and of a client transmitter-receiver 12, whichcommunicates with the base transmitter-receiver over a wireless channel14 via multicarrier signals (e.g., OFDM signals) while remainingsubstantially stationary relative to the base transmitter-receiver. Forexample, the base 10 may be a wireless router in a home or office, andthe client 12 may be a computer that communicates with the base via OFDMsignals that have N carriers. One or more antennas 16 are coupled to thebase 10, and one or more antennas 18 are coupled to the client 12. Eachantenna 16 may function as only a transmit antenna, as only a receiveantenna, or as a transmit-receive antenna; and each antenna 18 mayfunction similarly. Furthermore, the channel 14 may include Z multiplepaths L₀-L_(z−1) over which the multicarrier signals propagate. Forexample, a first path L₀ may be a straight-line path between theantennas 16 and 18, and a second path L₁ may be a multi-segmented paththat is caused by signal reflections from one or more objects (not shownin FIG. 1) near the base 10, client 12, or channel 14.

FIG. 2 is a frequency plot of some of the N carriers (here, carriers N−ato N−(a−8) are shown in solid line and are hereinafter called“subcarriers”) of an embodiment of an OFDM data symbol 20, which may betransmitted by the base 10 of FIG. 1 and received by the client 12, orvice versa—an OFDM data symbol is a portion of an OFDM signal that ismodulated with the same data subsymbols for a symbol period. Each of thesubcarriers N−a to N−(a−8) has a respective frequencyf_(N−a)-f_(N−(a−8)), and is orthogonal to the other subcarriers. In thiscontext, “orthogonal” means that, in the absence of inter-carrierinterference (discussed below) and noise, one may construct atime-domain signal from these modulated subcarriers (e.g., using anInverse Fast Fourier Transform (IFFT)), and then extract these modulatedsubcarriers, and the information that they carry, from the time-domainsignal (e.g., using a Fast Fourier Transform (FFT)) with no loss ofinformation. Furthermore, although the base 10 is described astransmitting the OFDM signal in the example below, it is understood thatthis example would be similar if the client 12 were transmitting theOFDM signal.

Referring to FIGS. 1 and 2, the transmitter of the base 10 modulateseach of at least some of the N subcarriers with a respective data value(hereinafter a data subsymbol) for a time period hereinafter called asymbol period—the transmitter may not use one or more of the Nsubcarriers due to, for example, excessive interference at thefrequencies of these subcarriers. Examples of suitable modulationschemes include binary phase-shift keying (BPSK), quadrature phase-shiftkeying (QPSK), and quadrature amplitude modulation (QAM), the latter twoschemes providing data subsymbols that each have multiple bits.

The frequency spacing f_(s) between adjacent ones of the N subcarriersis typically constant, and is conventionally selected to minimizeinter-carrier interference (ICI), which is a phenomenon that occurs ifenergy from one subcarrier “spills over” to the frequency slot ofanother subcarrier at the receiver of the client 12. At the transmitterof the base 10, each of the active ones of the N subcarriers has afrequency f_(k) (for k=0 to N−1) represented by a respective one of thesolid lines (only the frequencies f_(k) for k=N−a to N−(a−8) are shownin FIG. 2). But at the receiver of the client 12, the respectivefrequency f_(k) of each subcarrier may be effectively shifted within arespective frequency slot 22 indicated by the dashed lines (only theslots 22 of the frequencies f_(k) for k=N−a to N−(a−8) are shown in FIG.2). For example, at the receiver of the client 12, the frequency f_(N−a)of the subcarrier N−a may be shifted to another location within thefrequency slot 22 _(N−a), or may be “spread” over multiple locationswithin this frequency slot. Causes for this frequency shifting/spreadingmay include, for example, the existence of multiple transmission paths L(i.e., Z>1), and channel conditions (e.g., humidity, temperature) thatmay effectively shift the respective phase and attenuate the respectiveamplitude of each modulated subcarrier.

To allow the receiver of the client 12 to recover the data subsymbols inthe presence of ICI and other interference or noise, the transmitter ofthe base 10 transmits an OFDM training symbol—a “training symbol” is thecombination of all the training subsymbols transmitted during atraining-symbol period—shortly before transmitting an OFDM data symbol—a“data symbol” is the combination of all of the data subsymbolstransmitted during an OFDM data-symbol period. That is, the transmitterof the base 10 transmits the training symbol during a first OFDM symbolperiod, and transmits the data symbol during a second, subsequent OFDMsymbol period. Because the receiver of the client 12 “knows” theidentity of the transmitted training symbol ahead of time, the receivercharacterizes the channel 14 by comparing the received training symbolwith the known transmitted training symbol. For example, the receivermay characterize the channel 14 by generating an N×N matrix Ĥ ofestimated complex frequency-domain coefficients that respectivelyrepresent the estimated frequency response (e.g., the imparted ICI,amplitude attenuation, and phase shift) of the channel at each of thesubcarrier frequencies f_(k)—the “̂” indicates that Ĥ is an estimate ofthe actual channel matrix H. As discussed in more detail below, thereceiver may then use this channel-estimation matrix Ĥ to recovertransmitted data symbols from respective received data symbols.

FIG. 3 is a block diagram of an embodiment of the basetransmitter-receiver 10 and of the client transmitter-receiver 12 ofFIG. 1, but where the base and client are moving relative to one anotherat a non-zero velocity (the velocity may be constant or time varying)while they are communicating with one another, and where like numbersrefer to components common to FIGS. 1 and 3. For example, the base 10may be a cell tower, and the client 12 may be an internet-capable phonethat is located within a moving automobile 24. The base 10 and theclient 12 may communicate with one another according to one or morecommunications standards that specify OFDM technology for mobilecommunications. These standards include, for example, the DVB-H standardand the WiMAX standard. Furthermore, although only the client 12 isshown as moving, in other embodiments the base 10 may be moving and theclient 12 may be stationary, or both the base and the client may bemoving simultaneously.

FIG. 4 is a frequency plot of some of the N subcarriers (here,subcarriers N−a to N−(a−8) in solid line) of an embodiment of an OFDMsymbol 25 that may be transmitted by the base 10 of FIG. 1 and receivedby the client 12, or vice versa. Although the base 10 is described astransmitting the OFDM symbol in the example below, it is understood thatthis example would be similar if the client 12 were transmitting theOFDM symbol.

At the base 10, the OFDM symbol may be similar to the OFDM symbol ofFIG. 2 in that the base modulates each of at least some of the Nsubcarriers with a respective data subsymbol, and each of thedata-modulated ones of the N subcarriers has a center frequency f_(k)represented by a respective one of the solid lines.

But at the receiving client 12, the frequency f_(k) of a subcarrier kmay be shifted/spread by one or more times f_(s) as indicated by thefrequency slot 26 _(N−(a−4)) of the subcarrier k=N−(a−4) (only this onefrequency slot is shown in FIG. 3 for clarity) such that energy from asubcarrier k may spill over to the frequencies of one or more adjacentsubcarriers (e.g., k−1, k+1) on either side of the subcarrier k. Forexample, in the embodiment shown in FIG. 4, energy from the subcarrierk=N−(a−4) may spill over to the frequencies f_(N−a)-f_(N−(a−3)) andf_(N−(a−5))-f_(N−(a−8)) of the subcarriers k=N−a to N−(a−3) andk=N−(a−5) to N−(a−8).

The frequency shifts/spreads of the received OFDM subcarriers of FIG. 4may be significantly greater than the frequency shifts/spreads of thereceived OFDM subcarriers of FIG. 2 because, in addition to the causesfor this frequency shifting/spreading described above (e.g., theexistence of multiple transmission paths L and channel conditions), thereceived OFDM subcarriers of FIG. 4 may also experience respectiveDoppler shifts caused by the relative movement between the base 10 andthe client 12.

According to the Doppler Effect, the frequency of a signal at a receiveris different from the frequency of the signal at a transmitter if thereceiver and transmitter are moving relative to one another at anon-zero velocity. If the receiver and transmitter are moving away fromone another, then the frequency of the signal at the receiver istypically lower than the frequency of the signal at the transmitter;conversely, if the receiver and transmitter are moving toward oneanother, then the frequency of the signal at the receiver is typicallyhigher than the frequency of the signal at the transmitter. For example,a person (receiver) who is listening to the whistle of an approachingtrain (transmitter) may experience this phenomenon. While the train ismoving toward the person, the person perceives the whistle as having apitch (frequency) that is higher than the pitch that one on the trainwould perceive the whistle as having. But after the train passes theperson, and is thus moving away from him, the person perceives thewhistle as having a pitch lower than the pitch that one on the trainwould perceive the whistle as having.

Consequently, the subcarrier frequencies of the OFDM symbol 25 of FIG. 4may be influenced by the Doppler Effect in a similar manner at thereceiver of the client 12 of FIG. 3.

A measure of the influence that the Doppler Effect has on a singletransmitted tone (e.g., an unmodulated subcarrier signal with constant,non-zero amplitude) is the “Doppler Spread”, which is the bandwidth thatthe tone may occupy at the receiver due to the Doppler Effect. Forexample, suppose that the frequency of the tone is 1,000 Hz at thetransmitter, but that at the receiver, due to the non-zero velocity ofthe receiver relative to the transmitter, the received tone may have afrequency anywhere from 980 Hz to 1,020 Hz depending on theinstantaneous velocity. Therefore, in this example, the DopplerSpread=1020 Hz−980 Hz=40 Hz. That is, the Doppler Spread is (40Hz)/(1000 Hz)=4% of the frequency of the transmitted tone—althoughexpressed here in Hz and as a percentage of the transmitted frequency,the Doppler Spread may be expressed in other quantities as describedbelow.

For mobile OFDM devices, one may characterize the ICI caused by theDoppler Spread of a subcarrier in terms of the highest number ofadjacent subcarriers with which the subcarrier may interfere. Forexample, the total Doppler induced ICI caused by the 50^(th) (k=50)subcarrier is greater if energy from this subcarrier spills over to the48^(th), 49^(th), 51^(st), and 52^(nd) subcarriers, and is less ifenergy from this subcarrier spills over to only the 49^(th) and 51^(st)subcarriers. In actuality, because the Doppler Spread of a subcarriermay cause the subcarrier to spill over energy into many or all of theother N subcarrier slots to some degree, one may set a Doppler Spreadinterference threshold below which one subcarrier is deemed to beunaffected by the Doppler Spread of another subcarrier; such thresholdmay have units of, e.g., power or amplitude. Therefore, for a mobileOFDM device, the extent of Doppler induced ICI caused by a subcarrier kmay be defined in terms of the number of adjacent subcarriers (above andbelow the subcarrier k in question) that may experience a level of ICIabove the Doppler Spread interference threshold for the device.Furthermore, although in some applications one may assume that all ofthe subcarriers k experience the same Doppler Spread, in otherapplications, one may decide not to make this assumption.

Consequently, referring to FIGS. 3 and 4, the frequency slots 26 (onlythe frequency slot 26 _(N−(a−4)) of the subcarrier N−(a−4) is shown forclarity) each represent the bandwidth that a respective subcarriertransmitted by the base 10 may occupy at the receiving client 12 due toall causes (e.g., the existence of multiple transmission paths L,channel conditions, and Doppler Spread). But when the base 10 and client12 are moving relative to one another, the greatest contributor to thefrequency-slot bandwidth may be the Doppler Spread.

Still referring to FIGS. 3 and 4, because the Doppler Spread of an OFDMsignal may vary relatively quickly with time, transmitting a trainingsymbol separately from the data symbol may not allow the receiver of theclient 12 to adequately determine the channel-estimation matrix Ĥ forthe channel 14 as it exists while the OFDM data symbol is beingtransmitted.

Consequently, mobile OFDM devices, such as the base 10, may combinetraining subsymbols and data subsymbols into a single OFDM symbol suchthat a receiving device, such as the client 12, may characterize thechannel 14 for the same time period during which the data subsymbols aretransmitted.

FIG. 5 is a frequency plot of some of the N subcarriers k (here,subcarriers k=N−a to N−(a−12)) of an embodiment of an OFDM symbol 28,which may be transmitted by the base 10 of FIG. 3 and received by theclient 12 of FIG. 3, or vice versa, where the OFDM symbol includes bothtraining and data subsymbols. Although the base 10 is described astransmitting the OFDM signal in the example below, it is understood thatthis example would be similar if the client 12 were transmitting theOFDM signal.

The OFDM symbol 28 includes one or more clusters L_(D) of datasubcarriers, and one or more clusters L_(P) of training subcarriers,which are hereinafter called “pilot” subcarriers. The transmitter of thebase 10 may modulate the pilot subcarriers with respective pilotsubsymbols. In an embodiment, the data clusters L_(D) and the pilotclusters L_(P) are arranged in alternating fashion (i.e., one after theother) such that each data cluster L_(D) is separated from adjacent dataclusters by at least one pilot cluster L_(P), and such that each pilotcluster is separated from adjacent pilot clusters by at least one datacluster) within the OFDM symbol 28. As discussed below in conjunctionwith FIGS. 9-10B, because the client 12 receiver “knows” the pilotsubsymbols ahead of time, the client may use the pilot subsymbols tomore accurately estimate the channel 14 as it exists while the datasubsymbols are being transmitted.

In an embodiment, each data cluster L_(D) within the OFDM symbol 28includes a same first number (e.g., sixteen) of data subcarriers, andeach pilot cluster L_(P) within the OFDM symbol includes a same secondnumber (e.g., five or nine) of pilot subcarriers. For example, in theembodiment of FIG. 5, the illustrated pilot cluster L_(P) includes fivepilot subcarriers k=N−(a−3) to N−(a−7), and the other pilot clusters(not shown in FIG. 5) of the OFDM symbol 28 also each include fiverespective pilot subcarriers. But in another embodiment, a data clusterL_(D) may include a different number of data subcarriers than anotherdata cluster within the same OFDM symbol, and a pilot cluster L_(P) mayinclude a different number of pilot subcarriers than another pilotcluster within the same OFDM symbol. Furthermore, as discussed above,some of the data subcarriers may be unmodulated by a data subsymbol ormay have zero amplitude (i.e., zero energy), and, as discussed below inconjunction with FIGS. 7-8, some of the pilot subcarriers may beunmodulated by a pilot subsymbol or may have zero energy. Moreover, apilot cluster L_(P) or a data cluster L_(D) may “wrap around the ends”of the N subcarriers. For example, if there are N=128 subcarriers (k=0to 127), then a pilot cluster L_(P) may include five pilot subcarriersk=126, k=127, k=0, k=1, and k=2.

A designer of an OFDM receiver, such as the receiver in the client 12(FIG. 3), may select the minimum number N_(P) of pilot clusters L_(P) inthe OFDM symbol 28, and may select the minimum number L_(PN) of pilotsubcarriers k_(P) within each pilot cluster, for an intended applicationof the receiver based on the generally expected conditions of thecommunication channel 14 (FIG. 3) and on a desired data-error rate. Forexample, for an application where the receiver may be used in a movingautomobile, a designer may use the generally expected conditions of acommunication channel between a ground-based transmitter and receiverthat are moving relative to one another at speeds between approximately0 and 150 miles per hour (although non-racing automobiles rarely travelat speeds approaching 150 miles per hour, if the transmitter andreceiver are in respective automobiles that are moving in oppositedirections, then the speed of one automobile relative to the otherautomobile may approach or exceed 150 miles per hour). And to maximizethe number of data subcarriers in, and thus the data bandwidth of, theOFDM symbol 28, the designer may select the minimum number N_(P) ofpilot clusters L_(P), and the minimum number L_(PN) of pilot subcarriersk_(P) within each pilot cluster, that he/she predicts will allow thereceiver to estimate such a channel with an accuracy that is sufficientfor the receiver to recover data within the desired error rate.

FIG. 6 is a frequency plot of some of the N subcarriers k of anembodiment of the OFDM symbol 28 of FIG. 5, where the frequency (x) axisof FIG. 6 has a lower resolution than the frequency (x) axis of FIG. 5.

In an embodiment, the pilot clusters L_(P) are separated by a uniformseparation value P_(sep), which is the distance, measured in the numberof subcarriers k, between a pilot subcarrier in a pilot cluster and acorresponding pilot subcarrier in an adjacent pilot cluster. That is, apilot subcarrier that occupies a relative position within a pilotcluster L_(P) is P_(sep) subcarriers away from a pilot subcarrier thatoccupies the same relative position within an adjacent pilot cluster.For example, as shown in FIG. 6, the center pilot subcarrier (relativeposition 0) in pilot cluster L_(PS) is separated from the center pilotsubcarrier (also relative position 0) in the pilot cluster L_(PS+1) byP_(sep) subcarriers k. Also as shown in FIG. 6, the last pilotsubcarrier (relative position +2 in this example) in L_(PS+1) isseparated from the last pilot subcarrier (also relative position +2 inthis example) in the pilot cluster L_(PS+2) by P_(sep) subcarriers k.And, although not shown in FIG. 6, the very first pilot cluster L_(P0)in the OFDM symbol 28 is separated from the very last pilot clusterL_(P(Np−1)) in the OFDM symbol by P_(sep) when this separation iscalculated modulo N—calculating such separations modulo N yieldsaccurate separation values if a pilot cluster L_(P) or a data clusterL_(D) “wraps around the ends” of the N subcarriers as discussed above.

FIG. 7 is a frequency plot of an embodiment of a Frequency-DomainKronecker Delta (FDKD) pilot cluster L_(PFDKD) _(—) _(S).

Before substantive characteristics of the pilot cluster L_(PFDKD) _(—)_(S) are discussed, a convention for identifying a pilot cluster, suchas the pilot cluster L_(PFDKD) _(—) _(S), and its pilot subcarriers isdiscussed. In this convention, P_(b) identifies the relative location ofthe center subcarrier within the pilot cluster, S identifies therelative location of the pilot cluster within an OFDM symbol, W_(p) isthe total number of pilot subcarriers to the left and to the right ofthe center pilot subcarrier, B_(p) is the number of interior pilotsubcarriers to the left and to the right of the center pilot subcarrier,and W_(p)−B_(p) is the number of guard pilot subcarriers G_(p) at eachend of the pilot cluster. For example, if a pilot cluster L_(PFDKD) _(—)_(S) includes L_(PN)=5 total pilot subcarriers and two guard pilotsubcarriers, then W_(p)=(5−1)/2=2, B_(p)=W_(p)−G_(p)=2−1=1, and thepilot cluster L_(PFDKD) _(—) _(S) includes pilot subcarriers at thefollowing relative locations: P_(b)−2, P_(b)−1, P_(b), P_(b)+1, andP_(b)+2. And one may convert the relative-location identifiers intoabsolute-location identifiers by adding S·P_(sep) to each of therelative-location identifiers. So, continuing with the above example,the pilot cluster L_(PFDKD) _(—) _(S) includes pilot subcarriers at thefollowing absolute locations: P_(b)+S·P_(sep)−2, P_(b)+S·P_(sep)−1,P_(b)+S·P_(sep), P_(b)+S·P_(sep)+1, and P_(b)+S·P_(sep)+2. And,therefore, again in this example, the pilot cluster L_(PFDKD) _(—) _(S)includes the following pilot subcarriers: k_(Pb+S·Psep−2);k_(Pb+S·Psep−1); k_(Pb+S·Psep); k_(Pb+S·Psep+1); and k_(Pb+S·Psep+2).For example, if each pilot cluster L_(PFDKD) _(—) _(S) in an OFDM symbolincludes L_(PN)=5 pilot subcarriers, P_(sep)=8, and the first pilotsubcarrier of the zero^(th) pilot cluster L_(PFDKD) _(—) ₀ (S=0) is k₀,then P_(b)=2, W_(p)=2, and the sixth pilot cluster L_(PFDKD) _(—) ₆ (S=6and counting in a direction from the lowest to the highest subcarrierfrequency) includes the following pilot subcarriers: k₄₈, k₄₉, k₅₀, k₅₁,and k₅₂.

Still referring to FIG. 7, in an embodiment, the center subcarrierk_(Pb+S·Psep) (solid line in FIG. 7) of an FDKD pilot cluster L_(PFDKD)_(—) _(S) is modulated with a non-zero pilot subsymbol, and all of theother subcarriers (dashed lines) have zero energy; that is, all of theother subcarriers are effectively modulated with a zero pilot subsymbolequal to 0+j0. Therefore, in a FDKD pilot cluster L_(PFDKD) _(—) _(S),the only energy transmitted within the pilot cluster L_(PFDKD) _(—) _(S)is transmitted on the center subcarrier k_(Pb+S·Psep); the remainingsubcarriers in the pilot cluster are transmitted with zero energy. Butfor reasons discussed above in conjunction with FIG. 4, at the receiver,subcarriers of the pilot cluster L_(PFDKD) _(—) _(S) other than thecenter subcarrier may carry non-zero energy due to Doppler Spread. And,as discussed below in conjunction with FIGS. 9-10, the energy carried bythe interior pilot subcarriers at the receiver may allow the receiver togenerate an estimate of the communication channel as it exists duringtransmission of an OFDM symbol, where the estimate takes into accountICI caused by Doppler Spread. The guard pilot subcarriers are includedto provide a guard band that reduces to negligible levels the amount ofenergy from data subcarriers that “spills over” into the center andinterior pilot subcarriers, and vice-versa. One may select the totalnumber L_(PN) of pilot subcarriers and the number G_(P) of guard pilotsubcarriers in a pilot cluster L_(P) for a particular application basedon the expected Doppler Spread. Typically, the larger the expectedDoppler Spread, the larger the total number L_(PN) of pilot subcarriersand the number G_(p) of guard pilot subcarriers, and the smaller theexpected Doppler Spread, the smaller the total number L_(PN) of pilotsubcarriers and the number G_(p) of guard pilot subcarriers (G_(p) mayeven equal zero).

FIG. 8 is a frequency plot of an embodiment of an All-Pilot PilotCluster (APPC) L_(PAPPC) _(—) _(S). Unlike the FDKD pilot clusterL_(PFDKD) _(—) _(S) of FIG. 7 in which only the center subcarrierk_(Pb+S·Psep) is modulated with a non-zero pilot subsymbol, in an APPCpilot cluster L_(PAPPC) _(—) _(S), all of the pilot subcarriers (solidlines) k_(Pb+S·Psep−Wp)-k_(Pb+S·Psep+Wp) are modulated with a respectivenon-zero pilot subsymbol. That is, energy is transmitted on all of thepilot subcarriers k_(Pb+S·Psep−Wp)-k_(Pb+S·Psep+Wp) within an APPC pilotcluster. Furthermore, the pilot subcarriersk_(Pb+S·Psep−Wp)-k_(Pb+S·Psep+Wp) of an APPC pilot cluster may each bemodulated with the same, or with different, pilot subsymbols. Anddifferences between the transmitted pilot subsymbols (which are knownahead of time by the receiver) and the respective received pilotsubsymbols may allow the receiver to generate an estimate of thecommunication channel as it exists during transmission of an OFDMsymbol, where the estimate takes into account ICI caused by DopplerSpread.

FIG. 9 is a block diagram of an embodiment of a receiver 30 for a mobileOFDM device such as the base 10 or client 12 of FIG. 3.

The receiver 30 includes a receive antenna 32, a Fast Fourier Transform(FFT) unit 34, a channel estimator 36, a data-recovery unit 38, and adecoder 40. The FFT unit 34, channel estimator 36, data-recovery unit38, and decoder 40 may each be implemented in software, hardware, or acombination of software and hardware. For example, one or more of theFFT unit 34, the channel estimator 36, the data-recovery unit 38, andthe decoder 40 may be implemented on an integrated circuit (IC), andother components, such as a transmitter, may also be implemented on thesame IC, either on a same or different IC die. And this IC may becombined with one or more other ICs (not shown in FIG. 9) to form asystem such as the base 10 or client 12 of FIG. 3. Or, one or more ofthese components may be implemented by a software-executing controllersuch as a processor.

The receive antenna 32 may receive one or more OFDM symbols from atransmitter, such as the transmitter of the base 10 or client 12 of FIG.3, where at least some of the subcarrier signals may experience DopplerSpread. The antenna 32 may also function to transmit OFDM symbolsgenerated by a transmitter (not shown in FIG. 9) of the OFDM device thatincorporates the receiver 30. That is, the antenna 32 may function toboth receive and transmit OFDM symbols.

The FFT unit 34 conventionally converts a received OFDM symbol from atime-domain waveform into an N×1 column vector y of complexfrequency-domain coefficients (e.g., one complex coefficient for eachsubcarrier).

The channel estimator 36 estimates the response of the communicationchannel (e.g., the channel 14 of FIG. 3) from the coefficients of thevector y corresponding to the pilot subcarriers, which, as discussedabove in conjunction with FIGS. 5-8, are the subcarriers that composethe training portion of the received OFDM symbol. From thesepilot-subcarrier coefficients, the estimator 36 generates an N×Nchannel-estimation matrix Ĥ of complex frequency coefficients thatcollectively approximate the effective frequency response H of thecommunication channel—the effective frequency response may take intoaccount the affect of, e.g., channel conditions such as temperature andhumidity, the existence of multiple transmission paths, and the DopplerSpread, at each of the subcarrier frequencies f_(k). Because, asdiscussed above, the Doppler Spread may cause energy from one subcarrierto spill over into the frequency slot of another subcarrier at thereceiver 30, the matrix Ĥ may not be a diagonal matrix—a matrix isdiagonal if all of its elements are zero except for the elements thatlie along the main diagonal that extends from the top left corner of thematrix. An embodiment of the channel estimator 36, and an embodiment ofa technique for generating the channel-estimation matrix Ĥ, arediscussed below in conjunction with FIG. 10.

The data-recovery unit 38 recovers the data carried by the OFDM symbolas transmitted by generating an N×1 column vector {circumflex over (x)},which is an estimation of the transmitted OFDM data symbol. That is,{circumflex over (x)} includes complex coefficients (one for at leasteach data subcarrier) that are estimates of the complex coefficientswith which the transmitter modulated the transmitted data subcarriers.The unit 38 may generally recover {circumflex over (x)} according to thefollowing equations:

y=Ĥ{circumflex over (x)}+n  (1)

Ĥ ⁻¹(y)=Ĥ ⁻¹ Ĥ{circumflex over (x)}+Ĥ ⁻¹ n={circumflex over (x)}+Ĥ ⁻¹n  (2)

where n is an N×1 column vector of Additive-White-Gaussian-Noise (AWGN)complex coefficients at each of the subcarrier frequencies. Because, asdiscussed above, some of the y coefficients are for pilot subcarriersthat are used only for channel-estimation purposes, the elements of Ĥ,{circumflex over (x)}, y, and n that correspond to the N_(p)L_(PN) pilotsubcarriers (where N_(p) is the number of pilot clusters L_(P) in theOFDM symbol and L_(PN) is the number of pilot subcarriers per pilotcluster L_(P)) may be discarded prior to calculating Ĥ⁻¹ and solvingequation (2) so as to reduce the complexity, and increase the speed, ofthe calculation of {circumflex over (x)}. Examples of a data-recoveryunit and data-recovery techniques that may be used as and by thedata-recovery unit 38 are disclosed in U.S. patent application Ser. Nos.12/579,935 and 12/579,969, which were filed on Oct. 15, 2009 and whichare incorporated by reference. And conventional data-recovery units andtechniques that may be respectively used as and by the data-recoveryunit 38 also exist.

The data decoder 40 effectively uses the {circumflex over (x)}coefficients that correspond to the data subcarriers of the OFDM symbolto demodulate the corresponding data subsymbols, and to thus recover thedata represented by the subsymbols. For example, if the transmittermodulated a data subcarrier by mapping it to a respective QPSKconstellation element, then the data decoder 40 QPSK demodulates thedata subcarrier to recover the same constellation element, whichrepresents the bits of data carried by the modulated data subcarrier.

Still referring to FIG. 9, although conventional channel estimatorsexist, such a channel estimator may require a relatively long processingtime to determine the channel-estimation matrix Ĥ. For example, asignificant portion of the processing time consumed by a conventionalchannel estimator may be due to the calculating of one or more invertedmatrices in real time as part of the algorithm for determining Ĥ.

And referring to FIGS. 3 and 9, a conventional channel estimator mayalso be unable to account for changes in the number Z of the paths Lthat compose the communication channel 14, for changes in the respectivedelays of these paths, and for changes in the respective portions of theOFDM signal energy carried by these paths.

Over a period of time that may be much longer than a single OFDM symbolperiod (e.g., approximately 100-300 OFDM symbol periods), the number Zof paths L may change. The change in the number of paths L may be due tochanges in the channel conditions, such as changes in the number ofOFDM-signal-reflecting objects within or near the channel 14.

Furthermore, over the same period, the delays of the paths L, and theportions of the OFDM signal energy carried by the paths L, may alsochange. Each path L is defined by the delay it has relative to thezero^(th) path L₀ having zero delay. That is, the zero-delay path L₀ isthe path over which a version of an OFDM signal, having a respectiveportion of the energy of the transmitted OFDM signal, first reaches thereceiver; other versions of the OFDM signal reach the receiver over theremaining paths L at the respective delay times (relative to the delayof the path L₀) that define those paths, and with respective portions ofthe transmitted energy. The delay time of a path L may be defined inunits of the OFDM-signal sampling time employed by the receiver. Forexample, when a version of an OFDM signal propagates over a path L_(I)having a delay value of 1.0, this signal version first reaches thereceiver one sample time, or one sample, after the version of the OFDMsignal that is propagating over the path L₀ first reaches the receiver.Likewise, when a version of an OFDM signal propagates over a path L_(I)having a delay value of 3.5 samples, this signal version first reachesthe receiver three-and-one-half samples after the version of the OFDMsignal that is propagating over the path L₀ first reaches the receiver.To account for these delayed one or more paths L, the transmitter (notshown in FIG. 9) may add a cyclic prefix to the transmitted signal,where this prefix includes a number of samples, the aggregate delay ofwhich is at least as long as the longest path delay. For example, if thepath L with the longest delay has a delay of 3.5 samples, then thetransmitter may add a cyclic prefix of four samples to the transmittedsignal, such that the transmitted signal includes N+4 samples (as above,N is the total number of transmitted subcarriers k). These four extrasamples are actually the last four samples of the signal to betransmitted, and are effectively repeated at the beginning of the signaltransmission to be sure that by the time that the last signal samplearrives at the receiver over the zero^(th)-delay path L₀, the receiverhas also received over the remaining paths all of the samples of thesignal at least one time (because the signal is a periodic time-domainsignal, receiving a sample of the signal more than one time typicallyhas no negative affect at the receiver).

Unfortunately, a channel estimator that does not account for changes inat least one of the number, delays, and energies of the paths L may beunable to determine the channel-estimation matrix Ĥ with an accuracysufficient for some applications such as mobile OFDM.

FIG. 10 is a block diagram of the channel estimator 36 of FIG. 9, wherethe channel estimator may determine the channel-estimation matrix Ĥrecursively, without calculating the inverse of a matrix in real time(or otherwise), and by accounting for changes in the number, delays,and/or energies of the paths L that compose the communication channel 14(FIG. 3).

The estimator 36 includes a first stage 50 for determiningpath-independent quantities, b parallel second stages 52 ₀-52 _(b−1) forrespectively determining column vectors h_(l) ^((s)) that describe thetime-domain response of the Z paths L of the channel 14 (FIG. 3) duringa symbol period s, a communication-path monitor 54 for monitoring thenumber and delays of the channel paths L, and a channel-matrixcalculator 56 for determining the channel-estimation matrix Ĥ^((s)) forthe symbol period s.

The first stage 50 determines quantities that are independent of anyparticular channel path L, and that may be used by the second and thirdstages 52 and 56. Examples of, and techniques for determining, suchquantities are discussed below.

Each of the second stages 52 determines a respective time-domain pathvector h_(l) ^((s)) for a respective one of the Z paths I=L₀-I=L_(z−1).The number b of second stages 52 depends on the path delays that thechannel 14 (FIG. 3) may possibly have for a particular application. Forexample, suppose that even though it is anticipated that the channel 14will not have more than Z=4 simultaneous paths L during a symbol periods, the delays of these paths may range from 0 to 4 samples in incrementsof 0.25 samples, for a total of 4×1/(0.25)=16 possible path delays.Therefore, in such an example, the channel estimator 36 would includeb=16 second stages 52 ₀-52 ₁₅, one stage for each of the anticipatedsixteen path delays, respectively. As discussed below, the path monitor54 engages the second stages 52 corresponding to the delays of the pathsL present in the channel 14.

Each second stage 52 includes a first substage 58, a second substage 60,a third substage 62, and an engage/disengage switch 64.

Each first substage 58 is for determining quantities that are dependenton the particular channel path L associated with the second stage, andthat may be used by the corresponding second substage 60. Examples of,and techniques for calculating, such quantities are discussed below.

Each second substage 60 may include a respective recursive filter, suchas a Vector State Scalar Observation (VSSO) Kalman filter, which mayincrease the accuracy of the respective determined vector h_(l) ^((s))without increasing the complexity (or even reducing the complexity) ofthe channel estimator 36 as compared to prior channel estimators. Therecursive-filter substage 60 may increase the accuracy of h_(l) ^((s))by effectively using information from preceding symbol periods todetermine h_(l) ^((s)) for a current symbol period s. For example,referring to FIG. 3, suppose that the client 12 is moving at anapproximately constant velocity relative to the base 10; therefore, fromsymbol period to symbol period, one would expect the Doppler Spread tobe approximately the same. Without the recursive-filter substage 60, thesecond stage 52 may allow an anomaly, such as a noise “spike,” during asymbol period s to introduce a significant error into the path vectorh_(l) ^((s)), because the second stage has no way to “know” that theDoppler Spread is approximately constant relative to prior symbolperiods. But because the recursive-filter substage 60 may track thetrend (e.g., approximately constant Doppler Spread) of the response ofthe path L, it may allow the second stage 52 to lessen, or eveneliminate, the error that an anomaly may introduce into h_(l) ^((s)).Furthermore, one may design the recursive-filter stage 60 such that itdoes not perform a matrix inversion; for example, a VSSO Kalman filtermay be designed so that it does not perform a matrix inversion. This mayreduce the complexity of each second stage 52, and thus may reduce theoverall complexity of the channel estimator 36 as compared toconventional channel estimators. An embodiment of a recursive-filtersubstage 60 is described below.

Each third substage 62 determines the respective path vector h_(l)^((s)) in response to the second substage 60 as described below.

The communication-path monitor 54 tracks changes to the number, delays,and energies of the communication paths L, and periodically adjustswhich of the second stages 52 are engaged and disengaged based on thedelays and numbers of paths L that are currently present in the channel14 (FIG. 3). For example, if the path monitor 54 determines that thechannel 14 currently has Z=4 active paths L having relative delays of0.0 (the zero-delay path typically is always present), 0.25, 1.25, and2.0 respectively, then the path monitor engages the second stages 52corresponding to these delays via respective switches 64, and disengagesthe remaining second stages via respective switches 64. The path monitor54 determines which paths are active (i.e., present for purposes of thereceiver 30 of FIG. 9) by monitoring the energies of the paths andcomparing the energies to a path threshold. If a path's energy isgreater than the threshold, then the corresponding path isactive/present; otherwise, the corresponding path is inactive/notpresent. An embodiment of the path monitor 54 is further described inU.S. patent application Ser. No. 12/963,569, which is incorporated byreference.

The third stage 56 generates the channel-estimation matrix Ĥ in responseto the path vectors h_(l) ^((s)) from the second stages 52 that thecommunication-path monitor 54 engages.

An embodiment of the second recursive-filter substage 60 ₀ of the secondstage 52 ₀ is now described where the substage 60 ₀ includes a VSSOKalman filter, it being understood that the second substages 60 ₁-60_(b−1) may be similar.

The VSSO-Kalman-filter substage 60 ₀ includes an observation scalarcalculator 66 ₀, a state-vector predictor 68 ₀, amean-square-error-matrix predictor 70 ₀, a gain-vector calculator 72 ₀,a state-vector estimator 74 ₀, a mean-square-error-matrix updater 76 ₀,and a scaling-vector calculator 78 ₀; these components are describedbelow.

Before describing the operation of an embodiment of the channelestimator 36 of FIG. 10, some channel-estimation-related quantities, andthe mathematical relationships between some of these quantities, aredescribed. All of the quantities and relationships described belowassume that APPC pilot clusters (each including the same pilot symbolfrom pilot subcarrier to pilot subcarrier and from pilot cluster topilot cluster as discussed above in conjunction with FIG. 8) are usedunless otherwise noted.

h _(l) ^((s)) =[h _(l)( s ), . . . , h _(l)( s+N−1)]^(T)  (3)

where h_(l) ^((s)) is the column vector that represents the time-domainresponse of the path I=L during the s^(th) OFDM symbol period, s is thefirst sample time after the cyclic prefix (if there is a cyclic prefix)in the s^(th) OFDM symbol period, and N is the number of subcarriers k(both pilot and data subcarriers) in the transmitted OFDM signal. Forexample, if N=128, s=1 (2^(nd) OFDM symbol), and the cyclic prefix hasfour samples, then the transmitted OFDM signal carrying the 2^(nd) OFDMsymbol has a total of 128+4=132 samples, s represents the 268th sampletime (where the sample times are numbered continuously starting with the1^(st) OFDM symbol s=0), and h_(l) ^((s)) includes one hundred twentyeight complex elements corresponding to the samples 268-395.

In at least some applications, the elements of h_(l) ^((s)) may beapproximated as fitting a curve such as a straight line. Therefore, theelements of h_(l) ^((s)) may be represented in terms of a polynomialthat describes the curve. For example, where the curve is a straightline, which one may represent with the equation y=mx+b where m is theslope of the line and b is the y-axis intercept, h_(l) ^((s)) may besimilarly represented in terms of an offset and slope according to thefollowing equation:

h _(l) ^((s)) =B h _(l) ^((s))  (4)

where B is a binomial expansion matrix having elements m, n arranged inQ columns such that B(m,n)=m^(n) (m is the row number and n is thecolumn number), and h _(l) ^((s)) is a scaling column vector having Qrows/elements; consequently, where the fitting curve is a straight line,

$B = \begin{bmatrix}1 & 0 \\\vdots & \vdots \\1 & {N - 1}\end{bmatrix}$

and h _(l) ^((s)) is a column vector with Q=2 elements that respectivelyrepresent offset and slope. Because typically Q<<N, h _(l) ^((s)) istypically much smaller, and easier to manipulate, than h_(l) ^((s)).

The state vector g_(l) ^((S)) for the engaged filter substage 60corresponding to the I^(th) path during the symbol period s is given bythe following equation:

g _(l) ^((S)) =[ h _(l) ^((s−M+1)T)) , . . . , h _(l) ^((s)T)]^(T)  (5)

where M, an integer, is the filter prediction order that provides afilter substage 60 with its recursive feature. For example, to design afilter substage 60 for calculating the state vector g_(l) ^((S)) usinginformation from the current symbol period and the previous three symbolperiods, a designer would set M=4. Generally, the higher the predictionorder M, the more accurate the filter substage 60 but the longer itslatency; conversely, the lower the value of M, generally the lessaccurate the filter substage, but the shorter the latency.

The state equation for the engaged filter substage 60 corresponding tothe I^(th) path relates the I^(th) path during the current symbol periods to the same I^(th) path during one or more prior symbol periods, andis as follows:

g _(l) ^((S)) =Ag _(l) ^((s−1)) +e _(l) ^((s))  (6)

where A is an autoregressive matrix and e is the prediction-errorvector. A is dependent on the Doppler Spread, and, therefore, the firststage 50 may determine values of A ahead of time in a conventionalmanner and store these values in a lookup table (e.g., part of the firststage 50 or external thereto), which the first stage may access based onthe velocity of the receiver relative to the transmitter; for example,the receiver may determine this velocity using a GPS device.Alternatively, the channel estimator 36 may include a conventionallinear-adaptive filter (not shown in FIG. 10) that conventionally looksat the pilot symbols recovered by the receiver for one or more priorsymbol periods, predicts the pilot symbols to be recovered for thecurrent symbol period s based on the current velocity of the receiverrelative to the transmitter, and predicts the value of the A matrixbased on the previously recovered pilot symbols and the predicted pilotsymbols.

The prediction-error-correlation matrix G_(l) is given by the followingequation:

G _(l) =E{e _(l) ^((s)) e _(l) ^((s)H)}  (7)

Although the vector e_(l) ^((s)) may be unknown, its expectation (theright side of equation (7)), which may be generally described as anaverage of the change in the variance of e_(l) ^((s)) from symbol periodto symbol period, depends on the Doppler Spread, and, therefore, may beconventionally determined ahead of time through simulations or with aclosed-form expression; because this expectation is the same from symbolperiod s to symbol period s, G_(l) does not depend on s. Consequently,the first substage 58 may determine values for G_(l) dynamically orahead of time, and/or store these values of G_(l) in a lookup table withrespect to Doppler Spread, and may retrieve from the lookup table avalue of G_(l) for the current symbol period based on the velocity ofthe receiver relative to the transmitter during the current symbolperiod.

A path-dependent 1×(2w_(p)+1) row vector u_(I), which the first substage58 may calculate and/or store dynamically or ahead of time, is given bythe following equation:

$\begin{matrix}{u_{l} = \left\lbrack {^{- \frac{{j2\pi}\; w_{p}l}{N}}^{- \frac{{{j2\pi}{({w_{p} - 1})}}l}{N}}\ldots \mspace{14mu} 1\mspace{14mu} \ldots \mspace{20mu} ^{\frac{{j2\pi}\; w_{p}l}{N}}} \right\rbrack} & (8)\end{matrix}$

A path-independent matrix W, which the first stage 50 may calculateand/or store dynamically or ahead of time, is given by the followingequation:

$\begin{matrix}{W = \begin{bmatrix}{F^{H}\left( {{\langle{N + w_{p}}\rangle},\text{:}} \right)} \\{F^{H}\left( {{\langle{N + w_{p} - 1}\rangle},\text{:}} \right)} \\\vdots \\{F^{H}\left( {{\langle{N - w_{p}}\rangle},\text{:}} \right)}\end{bmatrix}} & (9)\end{matrix}$

where F is the known Fourier matrix, the

operator indicates a modulo N operation, and “:” indicates all columnsof the matrix F^(H) in the indicated rows. Note that the number of rowsin the W matrix is equal to the number of pilot subcarriers L_(PN) ineach transmitted/received pilot cluster L_(p).

A path-dependent 1×(MQ) row vector q_(l) ^(H), which the first substage58 may calculate and/or store dynamically or ahead of time, is given bythe following equation:

$\begin{matrix}{q_{l}^{H} = {\frac{{PN}_{p}}{N}\begin{bmatrix}0_{1{x{({M - 1})}}Q} & {u_{l}{WB}}\end{bmatrix}}} & (10)\end{matrix}$

where P is the pilot symbol (which is mapped to all pilot subcarriers inan embodiment) in the frequency domain, and 0_(1x(M−1)Q) is a row vectorhaving (M−1)Q columns/elements that are each equal to zero.

A path-independent N_(P)×Z Fourier matrix F_(L), which the first stage50 may calculate and/or store dynamically or ahead of time for theexpected values of Z, is given by the following equation:

F _(L) =F(p ⁽⁰⁾,0:Z−1)  (11)

where “p⁽⁰⁾” indicates that F_(L) includes the N_(P) rows of the Fouriermatrix F corresponding to the positions of the center pilot subcarriersof the pilot clusters L_(p) in the transmitted/received OFDM symbol, and“0:Z−1” indicates that F_(L) includes columns 0−Z−1 of F, where Z is thenumber of paths L present in the channel during the symbol period s.

The observation scalar y _(l) ^((s)) for the engaged filter substage 60corresponding to the I^(th) path is given by the following equation:

y _(l) ^((s)) =F _(L) ^(H)(l,:)y ^((s))(p ⁽⁰⁾)  (12)

where y^((s)) is the received-signal column vector in the frequencydomain during the symbol period s, and “p⁽⁰⁾” indicates thaty^((s))(p⁽⁰⁾) includes only the elements of y^((s)) that correspond tothe center pilot subcarriers of the transmitted/received pilot clustersL_(p). Although here only the center subcarrier of each pilot cluster isused to generate y _(l) ^((s)), other embodiments may use differentand/or more subcarriers within each pilot cluster to generate y _(l)^((s)).

The measurement equation for the engaged filter substage 60corresponding to the I^(th) path is given by the following equation:

y _(l) ^((s)) =q _(l) ^(H) g _(l) ^((s)) + n _(l) ^((s))  (13)

where n _(l) is the noise due to, e.g., interference on the pilotsubcarriers from the data subcarriers and Additive White Gaussian Noise(AWGN). Although n _(l) ^((s)) be unknown ahead of time, the firstsubstage 58 associated with the I^(th) path may compute itsexpectation/variance σ _(l) ²=E{| n _(l) ^((s))|²} dynamically or aheadof time by simulation or as a closed-form expression in a conventionalmanner, and may use σ _(l) ² as described below.

Referring to equation (12) and as further discussed below, themeasurement equation effectively relates the symbol recovered during thesymbol period s to the channel response during s, and, referring toequation (13) and also as further discussed below, the state equation(6), via the state vector g_(l) ^((s)), effectively modifies the resulty _(l) ^((s)) given by the measurement equation (12) based on thechannel response during one or more prior symbol periods. Furthermore,because y _(l) ^((s)) is a scalar, as discussed below, the filtersubstage 60 does not invert a matrix, which significantly reduces theoverall complexity of the channel estimator 36 as compared toconventional channel estimators.

Still referring to FIG. 10, the operation of an embodiment of thechannel estimator 36 is described in terms of the second stage 52 ₀, itbeing understood that the operations of the other second stages 52 maybe similar. Furthermore, in an embodiment, at least one path L having arelative delay of zero is always present in the channel 14 (FIG. 3), andthe second stage 52 ₀ is designed to determine h_(l=0) ^((s)) for theI=L₀=0 path having a delay of zero; therefore, in such an embodiment,the path monitor 54 always engages the second stage 52 ₀ for the pathI=L₀=0 having a delay of zero. Moreover, in the example below, theelements of h_(l) ^((s)) are fitted to a straight line as describedabove.

First, the path monitor 54 determines the number Z and correspondingdelays of the paths L that compose the channel 14 (FIG. 3), and engages,via the switches 64, the second stages 52 that correspond to thesepaths. As discussed above, for purposes of the following example, it isassumed that the path monitor 54 has engaged at least the second stage52 ₀.

Next, the first stage 50 may determine and/or store quantities (at leastsome of which are described above) that the second stage 52 ₀ may needfor its calculations, to the extent that the first stage has not alreadydetermined and/or stored these quantities.

Similarly, the first substage 58 ₀ may determine and/or store quantities(at least some of which are described above) that the filter substage 60₀ may need for its calculations, to the extent that the first substagehas not already determined and/or stored these quantities.

Next, the observation-scalar calculator 66 ₀ determines the observationscalar y _(l) ^((s)) for I=0 according to equation (12).

Then, the state-vector predictor 68 ₀ determines the predicted statevector

_(l) ^((s)) for I=0 according to the following equation:

_(l) ^((s)) =Aĝ _(l) ^((s−1))  (14)

Where s=0 (the initial symbol period), the predictor 68 ₀ also providesan initial value for ĝ_(l) ⁽⁻¹⁾. This initial value may be zero, or itmay be the expectation of ĝ_(l) ⁽⁻¹⁾. If the initial value is thelatter, the predictor 68 ₀ may compute the expectation of ĝ_(l) ⁽⁻¹⁾dynamically or ahead of time and store the computed expectation. Atechnique for calculating the expectation of ĝ_(l) ⁽⁻¹⁾ is described inS. M. Kay, “Fundamentals of Statistical Signal Processing: EstimationTheory,” Prentice Hall: New Jersey (1993), which is incorporated byreference. After the initial symbol period s=0, the state-vectorestimator 74 ₀ provides ĝ_(l) ^((s)), which becomes ĝ_(l) ^((s−1)) forthe next symbol period s as discussed below.

Next, the mean-square-error-matrix predictor 70 ₀ determines thepredicted mean-square-error matrix

_(l) ^((s)) for I=0 according to the following equation:

_(l) ^((s)) =A{circumflex over (θ)} _(l) ^((s−1)) A ^(H) +G _(l)  (15)

Where s=0 (the initial symbol period), the predictor 70 ₀ also providesan initial value for {circumflex over (θ)}_(l) ⁽⁻¹⁾. This initial valuemay be zero, or it may be the expectation of the error variance in thestate equation (6). If the initial value is the latter, then thepredictor 70 ₀ may compute the expectation of the error variance in thestate equation dynamically or ahead of time store the computedexpectation. A technique for calculating the expectation of the errorvariance in the state equation (6) is described in S. M. Kay,“Fundamentals of Statistical Signal Processing: Estimation Theory,”Prentice Hall: New Jersey (1993), which is incorporated by reference.After the initial symbol period s=0, the mean-square-error-matrixupdater 76 ₀ provides {circumflex over (θ)}_(l) ^((s)), which becomes{circumflex over (θ)}_(l) ^((s−1)) for the next symbol period s asdiscussed below.

Then, the gain-vector calculator 72 ₀ determines a gain vector Ω_(l)^((s)) for I=0 according to the following equation:

$\begin{matrix}{\Omega_{l}^{(s)} = \frac{{\overset{\Cup}{\theta}}_{l}^{(s)}q_{l}}{{\overset{\_}{\sigma}}_{l}^{2} + {q_{l}^{H}{\overset{\Cup}{\theta}}_{l}^{(s)}q_{l}}}} & (16)\end{matrix}$

Next, the state-vector estimator 74 ₀ generates the estimated statevector ĝ_(l) ^((s)) for I=0 according to the following equation:

ĝ _(l) ^((s))=

_(l) ^((s))+Ω_(l) ^((s)) [ y _(l) ^((s)) −q _(l) ^(H)

_(l) ^((s))]  (17)

As discussed above, ĝ_(l) ^((s)) is fed back to the state-vectorpredictor 68 ₀ to be used in equation (14) as ĝ_(l) ^((s−1)) for thenext symbol period.

Then, the mean-square-error-matrix updater 76 ₀ generates an updatedmean-square-error matrix {circumflex over (θ)}_(l) ^((s)) for I=0according to the following equation:

{circumflex over (θ)}_(l) ^((s)) =[I _(MQ)−Ω_(l) ^((s)) q _(l) ^(H)]

_(l) ^((s))  (18)

where I_(MQ) is an identity matrix of dimensions M(row)×Q(column).Furthermore, as discussed above, {circumflex over (θ)}_(l) ^((s)) is fedback to the mean-square-error-matrix predictor 70 ₀ to be used inequation (15) as {circumflex over (θ)}_(l) ^((s−1)) for the next symbolperiod.

Next, the scaling-vector calculator 78 ₀ determines the scaling vector h_(l) ^((s)) for I=0 and for a straight-line approximation of theelements of h_(l) ^((s)) according to one of the two followingequations:

h _(l) ^((s)) =ĝ _(l) ^((s))(MQ−Q:MQ−1)  (19)

h _(l) ^((s−M)) =ĝ _(l) ^((s))(0:Q−1)  (20)

Equation (19) may be referred to as the normal Kalman filter (NKF)output, and equation (20) may be referred to as the Kalman fixed-lagsmoother (KFLS) output, which is effectively a low-pass filtered output.Generally, the KFLS output is more accurate, but has a higher latency,than the NKF output.

Then, the third stage path-vector calculator 62 ₀ determines the pathvector h_(l) ^((s)) for I=0 according to equation (4) using either h_(l) ^((s)) from equation (19) or h _(l) ^((s−M)) from equation (20).

As stated above, the other engaged second stages 52 may operate in asimilar manner to generate h _(l) ^((s)) for the paths L₁≦I≦L_(Z−1) towhich they correspond. Typically, all engaged second stages 52 generateh _(l) ^((s)) according to equation (19) or equation (20) for a symbolperiod s, although it is contemplated that some second stages maygenerate h _(l) ^((s)) according to equation (19) while other secondstages may generate h _(l) ^((s)) according to equation (20) for asymbol period s.

Next, the third stage channel-matrix calculator 56 generates anintermediate channel-estimation matrix Ĥ ^((s)) from the path-responsevectors h_(l) ^((s)) for all of the paths L₀≦I≦L_(Z−1) that compose thechannel 14 (FIG. 3) according to the following equation:

Ĥ ^((s))(m,n)=ĥ _(<m−n>) ^((s))( s+m),for 0≦m≦N−1 and 0≦n≦N−1  (21)

Then, the third stage channel-matrix calculator 56 generates thechannel-estimation matrix Ĥ^((s)) according to the following equation:

$\begin{matrix}{{\hat{H}}^{(s)} = {\frac{1}{N}F\; {\underset{\_}{\hat{H}}}^{(s)}F^{H}}} & (22)\end{matrix}$

Still referring to FIG. 10, alternate embodiments of the channelestimator 36 are contemplated. For example, the functions contributed toany of the components of the channel estimator 36 may be performed inhardware, software, or a combination of hardware and software, where thesoftware is executed by a controller such as a processor. Furthermore,although described as VSSO Kalman filters, one or more of the secondsubstages 60 may be another type of recursive filter, for example,another type of recursive filter that is designed to perform no matrixinversions. Moreover, although described as operating in response toAPPC pilot clusters (FIG. 9), the channel estimator 36 may be modified(e.g., by modifying some or all of the above equations according toknown principles) to operate in response to FDKD pilot clusters (FIG.8). Furthermore, instead of, or in addition to, disengaging the unusedsecond stages 52, the path monitor 54 may cause these unused secondstages to enter a low- or no-power mode to save power.

Referring to FIGS. 1-10, as discussed above, an OFDM system such asshown in FIG. 3 forms a single multipath channel 14 between a singleantenna of the base 10 and a single antenna of client 12, where duringeach OFDM symbol period, the transmitting one of the base and clienttransmits one OFDM symbol over this channel.

To increase the data-transmission rate relative to an OFDM system suchas described above in conjunction with FIGS. 1-10, engineers havedeveloped a Multiple-Input-Multiple-Output (MIMO)-OFDM system that formsmultiple channels between the base and client, where, during each symbolperiod, the transmitting one of the base and client transmits arespective OFDM symbol from each of multiple transmit antennas using thesame N data and pilot subcarriers. For example, if a MIMO-OFDM systemuses three transmit antennas, then, for a given symbol period and valuefor N, the MIMO-OFDM system may transmit data at approximately threetimes the rate at which an OFDM system may transmit data, and may dothis using approximately the same bandwidth! And even though theMIMO-OFDM symbols include the same subcarrier-frequencies, a phenomenoncalled “spatial diversity” may allow the receiver to recover all of thetransmitted symbols with an error rate that is suitable for manyapplications.

FIG. 11 is a diagram of a MIMO-OFDM system 90, which includes a basetransmitter-receiver 92 and a client transmitter-receiver 94; thediagram is simplified to include only the antennas 96 and 98 of the baseand client, respectively. Furthermore, only the configuration/operationof the system 90 where the base 92 is the transmitter and the client 94is the receiver is discussed, it being understood that theconfiguration/operation of the system where the client is thetransmitter and the base is the receiver may be similar. Moreover, inthe described configuration of the system 90, although the client 94 mayinclude more than one antenna 98, it uses only one antenna for receivingsignals from the base 92. In addition, the base 92 and client 94 may bemoving relative to one another such that signals propagating between thebase and client may experience Doppler Spread.

The base 92 includes T antennas 96 ₀-96 _(T−1), and, in a transmittingconfiguration, transmits a respective OFDM signal carrying a respectiveOFDM symbol via each of these T antennas during a symbol period s,where, as discussed above, each OFDM signal includes the same Nsubcarriers. The combination of these simultaneous T OFDM signals may bereferred to as a MIMO-OFDM signal. Furthermore, the base 92 may includea respective transmitter for each antenna 96, or may include fewer thanT transmitters, at least some of which drive multiple ones of theantennas 96.

Therefore, in the described configuration, the system 90 forms Tmultipath transmit channels 100 ₀-100 _(T−1) between the respectivetransmit antennas 96 ₀-96 _(T−1) and the receive antenna 98. That is,the system 90 forms a respective channel 100 between each transmitantenna 96 ₀-96 _(T−1) and the single receive antenna 98. Furthermore,in an embodiment, the system 90 “assumes” that each channel 100 has thesame number Z of paths L.

Consequently, for a given symbol period s and number N of subcarriers,the MIMO-OFDM system 90 may transmit data at rate that is approximatelyT times the rate at which an OFDM system transmits data.

Because the channels 100 each include different paths L, the channelsmay be said to be spatially different or diverse. As discussed above andas evident from the equations discussed below in conjunction with FIG.14, even though the base 92 transmits the T OFDM signals using the sameN subcarriers, the spatial diversity of the channels 100 allows theclient 94 to recover each of the transmitted symbols with an error ratethat may be suitable for many applications, for example, mobileapplications where Doppler Spread may be present.

FIG. 12 is a diagram of a MIMO-OFDM system 110, which includes a basetransmitter-receiver 112 and a client transmitter-receiver 114; thediagram is simplified to include only the antennas 116 and 118 of thebase and client, respectively. Furthermore, only the configuration ofthe system 110 where the base 112 is the transmitter and the client 114is the receiver is discussed, it being understood that the configurationof the system where the client is the transmitter and the base is thereceiver may be similar. In addition, the base 112 and client 114 may bemoving relative to each other such that signals propagating between thebase and client may experience Doppler Spread.

A difference between the MIMO-OFDM system 110 and the MIMO-OFDM system90 of FIG. 11 is that in the system 110, the client 114 includes anduses R>1 antennas 118 to receive the OFDM signals that the base 112respectively transmits via the T transmit antennas 116; consequently,the system 110 forms T×R channels 120. In an embodiment of the system110, R≧T−1.

Although the multiple receive antennas R may not increase the data rate,they may increase the robustness of the system 110. For example,although each receive antenna 118 receives the same T OFDM signals fromthe transmit antennas 116, each receive antenna receives these T signalsover channels that are spatially diverse relative the channels overwhich the other receive antennas receive these signals. Therefore,although the OFDM signals received by one receive antenna 118 may carryOFDM symbols that are redundant relative to the OFDM symbols carried bythe OFDM signals received by the other receive antennas, the spatialdiversity of the channels over which the receive antennas receive thisredundant information may decrease the data error rate because theclient 114 has more diverse channels and paths from which to recover theT OFDM symbols. Furthermore, if one or more of the channels 120 betweenthe transmit antennas 116 and one of the receive antennas 118experiences catastrophic fading or other interference at a frequency ofone or more of the N subcarriers, then the client 114 may still be ableto recover the T transmitted OFDM symbols via one or more of the otherreceive antennas that receive the T OFDM signals over uncorruptedchannels.

FIG. 13 is a block diagram of an embodiment of a receiver 130 for amobile MIMO-OFDM device such as the base 92 or client 94 of FIG. 11, andsuch as the base 112 or client 114 of FIG. 12.

The receiver 130 includes R receive antennas 132 ₀-132 _(R−1), R FFTunits 134 ₀-134 _(R−1), a received-signal combiner 136, a channelestimator 138, a data-recovery unit 140, and a decoder 142. The FFTunits 134, combiner 136, channel estimator 138, data-recovery unit 140,and decoder 142 may each be implemented in software, hardware, or acombination of software and hardware. For example, one or more of theseitems may be implemented on an integrated circuit (IC), and othercomponents, such as a transmitter, may also be implemented on the sameIC, either on a same or different IC die. And this IC may be combinedwith one or more other ICs (not shown in FIG. 13) to form a system suchas the MIMO-OFDM system 90 of FIG. 11 or the MIMO-OFDM system 110 ofFIG. 12. Alternatively, the functions of one or more of these componentsmay be performed by a controller, such as a processor, executingsoftware instructions.

Each of the receive antennas 132 may receive OFDM singles from multipletransmit antennas, such as the T transmit antennas 96 of FIG. 11 or theT transmit antennas 116 of FIG. 12, where at least some of the Nsubcarrier signals may experience Doppler Spread. The receive antennas132 may also function to transmit collectively a MIMO-OFDM signalgenerated by a transmitter (not shown in FIG. 13) of the MIMO-OFDMdevice that incorporates the receiver 130. That is, the antennas 132 mayfunction to both receive and transmit MIMO-OFDM signals.

Each of the FFT units 134 ₀-134 _(R−1) conventionally converts arespective received MIMO-OFDM signal from a respective time-domainwaveform into a respective N×1 column vector y₀ ^((s))-y_(R−1) ^((s)) ofcomplex frequency-domain coefficients (e.g., one complex coefficient foreach subcarrier).

The combiner 136 combines the vectors y₀ ^((s))-y_(R−1) ^((s)) into asingle vector y^((s)). But if the device 130 has only R=1 receiveantennas 132, then the combiner 136 may be omitted, and the output ofthe single FFT unit 134 ₀ may be coupled to the y^((s)) input of thedata-recovery unit 140. An embodiment of the combiner 136 is discussedbelow in conjunction with FIG. 16.

The channel estimator 138 estimates the responses of all of thecommunication channels (e.g., the channels 100 ₀-100 _(T−1) of FIG. 11or the channels 120 ₀-120 _(TR−1) of FIG. 12) from the coefficients ofthe vectors y₀ ^((s))-y_(R−1) ^((s)) corresponding to the pilotsubcarriers, which, as discussed above in conjunction with FIGS. 5-8,are the subcarriers that compose the training portion of the receivedMIMO-OFDM symbol. From these pilot-subcarrier coefficients, theestimator 138 generates an N×NR matrix Ĥ^((a)) of complex frequencycoefficients that collectively approximate the effective frequencyresponse H^((s)) of all the communication channels combined—theeffective frequency response may take into account the affect of, e.g.,channel conditions such as temperature and humidity and the DopplerSpread at each of the subcarrier frequencies f_(k) in each of thechannels, and the existence of multiple transmission paths per channel.Because, as discussed above in conjunction with FIGS. 3-8, the DopplerSpread may cause energy from one subcarrier to spill over into thefrequency slot of another subcarrier at the receiver 130, the matrixĤ^((a)) may not be a diagonal matrix—a matrix is diagonal if all of itselements are zero except for the elements that lie along the maindiagonal that extends from the top left corner of the matrix. Anembodiment of the channel estimator 138, and an embodiment of atechnique for generating the channel-estimation matrix Ĥ^((a)), arediscussed below in conjunction with FIGS. 14-15.

The data-recovery unit 140 recovers the data carried by the MIMO-OFDMsymbol as transmitted by generating a TN×1 column vector {circumflexover (x)}^((a)), which is an estimation of the transmitted MIMO-OFDMsymbol, which is equivalent to T OFDM symbols. That is, {circumflex over(x)}^((a)) includes complex coefficients (one for at least each datasubcarrier) that are estimates of the complex coefficients with whichthe transmitter(s) modulated the transmitted subcarriers. The unit 140may generally recover {circumflex over (x)}^((a)) according to equations(1) and (2) above. Because, as discussed above in conjunction with FIGS.3-8, some of the y^((s)) coefficients are for pilot subcarriers that areused only for channel-estimation purposes, the elements of Ĥ^((a)),{circumflex over (x)}^((a)), y^((s)), and n^((s)) that correspond to theTN_(p)L_(PN) pilot subcarriers (where TN_(P) is the number of pilotclusters L_(p) in the MIMO-OFDM symbol, and L_(PN) is the number ofpilot subcarriers within each pilot cluster L_(p)) may be discardedprior to calculating Ĥ^((s)) ⁻¹ and solving equation (2) so as to reducethe complexity, and increase the speed, of the calculation of{circumflex over (x)}^((a)). Examples of a data-recovery unit 140 anddata-recovery techniques that may be used as and by the data-recoveryunit are disclosed in U.S. patent application Ser. Nos. 12/579,935 and12/579,969, which were filed on Oct. 15, 2009 and which are incorporatedby reference. And conventional data-recovery units and techniques thatmay be respectively used as and by the data-recovery unit 140 alsoexist.

The data decoder 142 effectively uses the {circumflex over (x)}^((a))coefficients that correspond to the data subcarriers of the MIMO-OFDMsymbol to demodulate the corresponding data subsymbols, and to thusrecover the data represented by the subsymbols. For example, if atransmitter modulated a data subcarrier by mapping it to a respectiveQPSK constellation element, then the data decoder 142 QPSK demodulatesthe data subcarrier to recover the same constellation element, whichrepresents the bits of data carried by the modulated data subcarrier.

Still referring to FIG. 13, although conventional MIMO-OFDM channelestimators exist, such a channel estimator may require a relatively longprocessing time to determine Ĥ^((a)). For example, a significant portionof the processing time consumed by a conventional channel estimator maybe due to the calculating of one or more inverted matrices in real timeas part of the algorithm for determining Ĥ^((a)).

And referring to FIGS. 11, 12, and 13, and as discussed above inconjunction with FIG. 9, a conventional channel estimator may also beunable to account for changes in the number of the paths L that composethe communication channels 100 or 120, for changes in the respectivedelays of these paths, and for changes in the respective portions of theMIMO-OFDM signal energy carried by these paths.

Unfortunately, a channel estimator that does not account for changes inat least one of the number, delays, and energies of the paths L may beunable to determine the channel-estimation matrix Ĥ^((a)) with anaccuracy sufficient for some applications such as mobile MIMO-OFDM.

FIG. 14 is a block diagram of an embodiment of a portion 148 of thechannel estimator 138 of FIG. 13 corresponding to one transmit antennaand one receive antenna (e.g., receive antenna 132 _(R−1) of FIG. 13)where i is the transmit-antenna index, r is the receive-antenna index,and the channel estimator may determine the partial channel-estimationmatrices Ĥ_(r) ^((i,s)): (1) recursively without calculating the inverseof a matrix at least in real time, and (2) by accounting for changes inthe number, delays, and/or energies of the paths L that compose thecommunication channels corresponding to the receive antenna. It iscontemplated that the portions 148 of the channel estimator 138corresponding to the other transmit antennas T and to the other receiveantennas 132 (if there is more than one receive antenna) may be similar.

The portion 148 of the channel estimator 138 determines the partialchannel-estimation matrix Ĥ_(r) ^((i,a)) for the communication channelbetween the i^(th) transmit antenna (e.g., a transmit antenna 116 inFIG. 12) and the r^(th) receive antenna (e.g., a receive antenna 132 inFIG. 13); therefore, for T transmit antennas and R receive antennas, thechannel estimator 138 includes R×T portions that may be similar to theportion 148. For example, if R=T=2, then the channel estimator 138 mayinclude 2×2=4 respective portions 148 for the following channels: (i=0,r=0), (i=1, r=0), (i=0, r=1), and (i=1, r=1). An embodiment of acombiner for combining the R×T partial channel-estimation matrices Ĥ_(r)^((i,a)) into a channel-estimation matrix Ĥ^((a)) is described below inconjunction with FIG. 15.

The partial channel-estimator portion 148 includes a first stage 150 fordetermining path-independent quantities for the communication channelbetween the transmit antenna and r^(th) receive antenna (hereinafter the(r,i) channel), b parallel second stages 152 ₀-152 _(b−1) forrespectively determining column vectors h_(r,l) ^((i,s)) that describethe time-domain responses of the Z paths L of the (r,i) channel duringthe symbol period s, a communication-path monitor 154 for monitoring thenumber and delays of the Z channel paths L, and a partial channel-matrixcalculator 156 for determining the partial channel-estimation matrixĤ_(r) ^((i,s)) for the (r,i) channel during the symbol period s.

The first stage 150 determines quantities that are related to the (r,i)channel but that are independent of any particular channel path L, andthat may be used by the second and third stages 152 and 156. Examplesof, and techniques for determining, such quantities are discussed below.Furthermore, if such a quantity is also independent of either thereceive antenna r or the transmit antenna i, then the first stage 150may provide such quantity to one or more first stages of the otherchannel-estimator portions 148, or receive such quantity from a firststage of another channel-estimator portion, to reduce or eliminateredundant processing.

Each of the second stages 152 determines a respective time-domain pathvector h_(r,l) ^((i,s)) for a respective one of the Z pathsL₀≦I≦L_(z−1). The number b of second stages 152 depends on the pathdelays that the (r,i) channel may possibly have for a particularapplication. For example, suppose that even though it is anticipatedthat the (r,i) channel will not have more than Z=4 simultaneous paths Lduring a symbol period s, the delays of these paths may range from 0 to4 samples in increments of 0.25 samples, for a total of 4×1/(0.25)=16possible path delays. Therefore, in such an example, thepartial-channel-estimator portion 148 would include b=16 second stages152 ₀-152 ₁₅, one stage for each of the anticipated sixteen path delays,respectively. As discussed below, the path monitor 154 engages thesecond stages 152 corresponding to the delays of the paths L present inthe (r,i) channel.

Each second stage 152 includes a first substage 158, a second substage160, a third substage 162, and an engage/disengage switch 164.

Each first substage 158 is for determining quantities that are dependenton the particular channel path L of the (r,i) channel associated withthe second stage, and that may be used by the corresponding secondsubstage 160. Examples of, and techniques for calculating, suchquantities are discussed below. Furthermore, if such a path-dependentquantity is independent of the receive antenna r or transmit antenna i,then the first substage 158 may provide such quantity to one or morefirst substages of the other channel-estimator portions 148, or receivesuch quantity from a first substage of another channel-estimatorportion, to reduce or eliminate redundant processing.

Each second substage 160 may include a respective recursive filter, suchas a Vector State Scalar Observation (VSSO) Kalman filter, which mayincrease the accuracy of the respective determined vector h_(r,l)^((i,s)) without increasing the complexity (or even reducing thecomplexity) of the channel estimator 138 as compared to prior channelestimators. The recursive-filter substage 160 may increase the accuracyof h_(r,l) ^((i,s)) by effectively using information from precedingsymbol periods to determine h_(r,l) ^((i,s)) for a current symbol periods. For example, referring to FIG. 12, suppose that the client 114 ismoving at an approximately constant velocity relative to the base 112;therefore, from symbol period to symbol period, one would expect theDoppler Spread to be approximately the same. Without therecursive-filter substage 160, the second stage 152 may allow ananomaly, such as a noise “spike,” during a symbol period s to introducea significant error into the path vector h_(r,l) ^((i,s)), because thesecond stage has no way to “know” that the Doppler Spread isapproximately constant relative to prior symbol periods. But because therecursive-filter substage 160 may track the trend (e.g., approximatelyconstant Doppler Spread) of the response of the path L, it may allow thesecond stage 152 to lessen, or even eliminate, the error that an anomalymay introduce into h_(r,l) ^((i,s)). Furthermore, one may design therecursive-filter stage 160 such that it does not perform a matrixinversion, at least not in real time; for example, a VSSO Kalman filterdoes not perform a matrix inversion in real time. This may reduce thecomplexity of each second stage 152, and thus may reduce the overallcomplexity of the channel estimator 138 as compared to conventionalchannel estimators. An embodiment of a recursive-filter substage 160 isdescribed below.

Each third substage 162 determines the respective path vector h_(r,l)^((i,s)) in response to the second substage 160 as described below.

The communication-path monitor 154 tracks changes to the number, delays,and energies of the communication paths L in the (r,i) channel, andperiodically adjusts which of the second stages 152 are engaged anddisengaged based on the delays and numbers of paths L that are currentlypresent in the channel. For example, if the path monitor 154 determinesthat the (r,i) channel currently has Z=4 active paths L having relativedelays of 0.0 (the zero-delay path typically is always present), 0.25,1.25, and 2.0 respectively, then the path monitor engages the secondstages 152 corresponding to these delays via the respective switches164, and disengages the remaining second stages via respective switches164. The path monitor 154 determines which paths are active (i.e.,present for purposes of the receiver 130 of FIG. 13) by monitoring theenergies of the paths and comparing the energies to a path threshold. Ifa path's energy is greater than the threshold, then the correspondingpath is active/present; otherwise, the corresponding path isinactive/not present. An embodiment of the path monitor 154 is furtherdescribed in U.S. patent application Ser. No. 12/963,569, which isincorporated by reference.

The third stage 156 generates the partial channel-estimation matrixĤ_(r) ^((i,a)) in response to the path vectors h_(r,l) ^((i,s)) from thesecond stages 152 that the communication-path monitor 154 engages.

An embodiment of the second recursive-filter substage 160 ₀ of thesecond stage 152 ₀ is now described where the substage 160 ₀ includes aVSSO Kalman filter, it being understood that the second substages 160₁-160 _(b−1) may be similar.

The VSSO-Kalman-filter substage 160 ₀ includes an observation scalarcalculator 166 ₀, a state-vector predictor 168 ₀, amean-square-error-matrix predictor 170 ₀, a gain-vector calculator 172₀, a state-vector estimator 174 ₀, a mean-square-error-matrix updater176 ₀, and a scaling-vector calculator 178 ₀; these components aredescribed below.

Before describing the operation of an embodiment of the partialchannel-estimator portion 148 of FIG. 14, some MIMO-OFDMchannel-estimation-related quantities, and the mathematicalrelationships between some of these quantities, are described. All ofthe quantities and relationships described below assume that: (1) APPCpilot clusters L_(p) (FIG. 8) are used unless otherwise noted (anembodiment of a pilot-symbol pattern that is compatible with the channelestimator 138 (FIG. 13) is discussed below in conjunction with FIG. 17);(2) the pilot clusters L_(p) in each OFDM signal from a respectivetransmit antenna are in the same relative positions (i.e., include thesame subcarriers); and (3) each of the R×T channels includes the samenumber Z of paths L.

h _(r,l) ^((i,s)) =[h _(r,l) ^((i,s))( s ), . . . , h _(r,l) ^((i,s))(s+N−1)]^(T)  (23)

where h_(r,l) ^((i,s)) is the column vector that represents thetime-domain response of the path I of the (r,i) channel during thes^(th) MIMO-OFDM symbol period, s is the first sample time after thecyclic prefix in the s^(th) OFDM symbol (if there is a cyclic prefix),and N is the number of subcarriers k (both pilot and data subcarriers)in the OFDM signal transmitted by the i^(th) transmit antenna. Forexample, if N=128, s=1 (the symbol period after the 0^(th) symbolperiod) and the cyclic prefix has four samples, then the OFDM signaltransmitted by the i^(th) transmit antenna has a total of 128+4=132samples, s represents the 268 sample time, and h_(r,l) ^((i,s)) includesone hundred twenty eight complex elements corresponding to the samples268-395.

In at least some applications, the elements of h_(r,l) ^((i,s)) may beapproximated as fitting a curve such as a straight line. Therefore, theelements of h_(r,l) ^((i,s)) may be represented in terms of a polynomialthat describes the curve. For example, where the curve is a straightline, which one may represent with the equation y=mx+b where m is theslope of the line and b is the y-axis intercept, h_(r,l) ^((i,s)) may besimilarly represented in terms of an offset and slope according to thefollowing equation:

h _(r,l) ^((i,s)) =B h _(r,l) ^((i,s))  (24)

where B is a binomial expansion matrix having elements (m, n) arrangedin Q columns such that B(m,n)=m^(n) (m is the row number and n is thecolumn number), and h _(r,l) ^((i,s)) is a scaling column vector havingQ rows/elements; consequently, where the fitting curve is a straightline

$B = \begin{bmatrix}1 & 0 \\\vdots & \vdots \\1 & {N - 1}\end{bmatrix}$

and h _(r,l) ^((i,s)) is a column vector with Q=2 elements thatrespectively represent offset and slope. Because typically Q<<N, h_(r,l) ^((i,s)) is typically much smaller (e.g., has many fewerelements), and is thus easier to manipulate, than h_(r,l) ^((i,s)).

The state vector g_(r,l) ^((i,s)) for the engaged filter substage 160corresponding to the I^(th) path of the (r,i) channel during the symbolperiod s is given by the following equation:

g _(r,l) ^((i,s)) =[ h _(r,l) ^((i, s−M+1)T) , . . . , h _(r,l)^((i,s)T)]^(T)  (25)

where M, an integer, is the filter prediction order that provides afilter substage 160 with its recursive feature. For example, to design afilter substage 160 for calculating the state vector g_(r,l) ^((i,s))using information from the current symbol period and the previous threesymbol periods, a designer would set M=4. Generally, the higher theprediction order M, the more accurate the filter substage 160 but thelonger its latency, and the lower the value of M, the less accurate thefilter substage but the shorter its latency.

The state equation for the engaged filter substage 160 corresponding tothe I^(th) path of the (r,i) channel relates the I^(th) path during thecurrent symbol period s to the same I^(th) path during one or more priorsymbol periods, and is as follows:

g _(r,l) ^((i,s)) =Ag _(r,l) ^((i, s−1)) +e _(r,l) ^((i,s))  (26)

where A is an autoregressive matrix and e is the prediction-errorvector. A is dependent on the Doppler Spread, and, therefore, the firststage 150 may determine values of A ahead of time in a conventionalmanner and store these values in a lookup table, which the first stagemay access based on the velocity of the receiver relative to thetransmitter; for example, a receiver such as the receiver 130 (FIG. 13)may determine this velocity using a GPS device. Alternatively, thechannel estimator 138 may include a conventional linear-adaptive filter(not shown in FIG. 14) that conventionally looks at the pilot symbolsrecovered by the receiver for one or more prior symbol periods, predictsthe pilot symbols to be recovered for the current symbol period s basedon the current velocity of the receiver relative to the transmitter, andpredicts the value of the A matrix based on the previously recoveredpilot symbols and the predicted pilot symbols.

The prediction-error-correlation matrix G_(r,l) ^((i)) is given by thefollowing equation:

G _(r,l) ^((i)) =E{e _(r,l) ^((i,s)) e _(r,l) ^((i,s)H)}  (27)

Although the vector e_(r,l) ^((i,s)) may be unknown, its expectation(the right side of equation (27)), which may be generally described asan average of the change in the variance of e_(r,l) ^((i,s)) from symbolperiod to symbol period, depends on the Doppler Spread, and, therefore,may be conventionally determined ahead of time through simulations orwith a closed-form expression. Furthermore, because this expectation isapproximated to be the same from symbol period to symbol period, theleft side of equation (27) is independent of the symbol period s.Consequently, the first substage 158 may determine values for G_(r,l)^((i)) dynamically or ahead of time and/or store these values of G_(r,l)^((i)) in a lookup table with respect to Doppler Spread, and mayretrieve from the lookup table a value of G_(r,l) ^((i)) for the currentsymbol period based on the velocity of the receiver relative to thetransmitter during the current symbol period.

A channel-independent N_(p)×1 column vector P_(p) ^(a), which the firstsubstage 158 may calculate and/or store dynamically or ahead of time, isgiven by the following equation:

P _(p) ^(a) =[P _(b) +a,P _(b) +P _(sep) +a, . . . , P _(b)+(N _(p)−1)P_(sep) +a]  (28)

where, as discussed above in conjunction with FIGS. 7-8, P_(b) is therelative center pilot subcarrier of each pilot cluster L_(p) (and,therefore, is the center pilot subcarrier of the first pilot clusterL_(p)), P_(sep) is the pilot-cluster separation, and N_(p) is the numberof pilot clusters in an OFDM signal transmitted by each transmitantenna. For example, if a signal has N_(p)=3 pilot clusters of L_(PN)=5pilot subcarriers each, P_(b)=2, and P_(sep)=8, then P_(P) ⁻²=[0, 8,16], P_(P) ⁻¹=[1, 9, 17], P_(p) ⁰=[2, 10, 18], P_(p) ⁺¹=[3, 11, 19], andP_(p) ⁺²=[4, 12, 20].

A transmit-antenna-dependent 1×L_(p) row vector P_(cluster) ^((i,c)),which the first substage 158 may store ahead of time, is defined as thec^(th) pilot cluster L_(P) transmitted by the i^(th) transmit antenna.For example, where c=0, then the elements of P_(cluster) ^((i,0))include the pilot symbols of the 0^(th) pilot cluster L_(p) transmittedby the i^(th) transmit antenna. The first substage 158 may generateand/or store the vectors P_(cluster) ^((i,c)) because the receiver 130(FIG. 13) “knows” the pilot symbols and pilot-cluster locations ahead oftime.

A transmit-antenna-dependent value P^((i,k)), which the first substage158 may store ahead of time, is the pilot symbol (e.g., in the frequencydomain) transmitted from the i^(th) antenna on the k^(th) subcarrier.

A transmit-antenna-dependent pilot-pattern matrix P_(pat) ^((i)) ofdimensions N_(p)×L_(PN), which the first substage 158 may determineand/or store ahead of time, is given by the following equation:

$\begin{matrix}{P_{pat}^{(i)} = \begin{bmatrix}P_{cluster}^{({i,0})} \\\vdots \\P_{cluster}^{({i,{N_{p} - 1}})}\end{bmatrix}} & (29)\end{matrix}$

where, the first row of P_(pat) ^((i)) includes the pilot symbols thatcompose the 0^(th) pilot cluster L_(p) transmitted from the i^(th)transmit antenna, the second row of P_(pat) ^((i)) includes the pilotsymbols that compose the 1^(st) pilot cluster L_(p) transmitted from thei^(th) transmit antenna, and the (N_(p)−1)^(th) row of P_(pat) ^((i))includes the pilot symbols that compose the (Np−1)^(th) pilot clusterL_(p) transmitted from the i^(th) transmit antenna. In an embodiment,the rows of P_(pat) ^((i)) may be shifted up or down as long as theyremain in a sequence 0−N_(p)−1 and the same shift is applied to all ofthe matrices P_(pat) ^((i)) for 0≦i≦T−1 (where T is the number oftransmit antennas).

A channel-independent matrix Q (not to be confused with the value Qdescribed above) having the same dimensions N_(p)×L_(PN) as P_(pat)^((i)) and which may be stored by the first substage 158 ahead of time,is given by the following equation:

$\begin{matrix}{Q = \begin{bmatrix}{P_{b} - w_{p}} & \ldots & {P_{b} + w_{p}} \\\; & \vdots & \; \\{P_{b} + {P_{sep}\left( {N_{p} - 1} \right)} - w_{p}} & \ldots & {P_{b} + {P_{sep}\left( {N_{p} - 1} \right)} + w_{p}}\end{bmatrix}} & (30)\end{matrix}$

That is, the matrix Q includes the subcarrier indices k for the pilotsymbols in P_(pat) ^((i)). For example, if a transmitted signal hasN_(p)=3 pilot clusters of L_(PN)=5 pilot subcarriers each, P_(b)=2, andP_(sep)=8, then Q would equal

$\begin{bmatrix}0 & 1 & 2 & 3 & 4 \\8 & 9 & 10 & 11 & 12 \\16 & 17 & 18 & 19 & 20\end{bmatrix}.$

A channel-independent (assuming all pilot clusters are in the samerelative positions in all i transmitted OFDM signals) column vectorP_(Q) having dimensions N_(p)L_(PN)×1 and which the first substage 158may determine and/or store ahead of time, is given by the followingequation:

P _(Q) =[k _(P) _(b−) _(w) _(p) . . . k _(P) _(b+) _(P) _(sep) _((N)_(p) _(−1)+w) _(p) ]^(T)  (31)

That is, P_(Q) includes the subcarrier indices k of all pilotsubcarriers in an OFDM symbol; or, viewed another way, P_(Q) includesthe rows of the matrix Q transposed and “stacked” end to end.

A transmit-antenna- and path-dependent 2N_(p)×L_(PN) matrix θ _(l)^((i)), which the first substage 158 may determine and/or store ahead oftime, is given by the following equation:

$\begin{matrix}{{\underset{\_}{\theta}}_{l}^{(i)} = \begin{bmatrix}^{{- j}\; 2\pi \; Q\; \Delta \; {fl}} & \odot & p_{pat}^{(i)} \\^{{- j}\; 2\pi \; Q\; \Delta \; {fl}} & \odot & p_{pat}^{(i)}\end{bmatrix}} & (32)\end{matrix}$

where

${\Delta \; f} = \frac{1}{N}$

and the “⊙” operator indicates that each e term is formed using arespective element of the matrix Q, each formed e term is multiplied bya corresponding element of the matrix p_(pat) ^((i)), and this procedureis repeated for all N_(p)×L_(PN) elements of Q and p_(pat) ^((i)),resulting in another N_(p)×L_(PN) matrix. Then, this resulting matrix iseffectively “stacked” on itself to obtain the 2N_(p)×L_(PN) matrix θ_(l) ^((i)).

N_(p) transmit-antenna- and path-dependent N_(p)×L_(PN) matrices R_(l)^((i,u)), which the first substage 158 may determine and/or store aheadof time, are given by the following equation for 0≦u≦N_(p)−1:

R _(l) ^((i,u))=θ _(l) ^((i))(u→u+Np−1,:)  (33)

where “u→u+Np−1” are the rows of θ _(l) ^((i)) used to populate R_(l)^((i,u)) and “:” indicates that all columns of these rows of θ _(l)^((i)) are used to populate R_(l) ^((i,u)).

A transmit-antenna- and path-dependent N_(p)×N_(p)L_(PN) matrix θ_(l)^((i)) (note there is no underline beneath “θ”, this lack of anunderline distinguishing this matrix from the matrix θ _(l) ^((i)) ofequation (32)), which the first substage 158 may determine and/or storeahead of time, is given by the following equation:

θ_(l) ^((i)) =[R _(l) ^((i,0)) R _(l) ^((i,1)) . . . R _(l) ^((i, N)^(p) ⁻¹⁾]  (34)

j channel-independent N_(p)L_(PN)×N matrices W^((j)), which the firststage 150 may calculate and/or store dynamically or ahead of time, isgiven by the following equation for −B_(p)≦j≦+B_(p):

$\begin{matrix}{W^{(j)} = \begin{bmatrix}{F^{H}\left( {{\langle{N + \left( {{P_{Q}(0)} - P_{b} - j} \right)}\rangle},:} \right)} \\{F^{H}\left( {{\langle{N + \left( {{P_{Q}(1)} - P_{b} - j} \right)}\rangle},:} \right)} \\{F^{H}\left( {{\langle{N + \left( {{P_{Q}\left( {{N_{P}L_{PN}} - 1} \right)} - P_{b} - j} \right)}\rangle},:} \right)}\end{bmatrix}} & (35)\end{matrix}$

where F is the known Fourier matrix, the “

” operator indicates a modulo N operation, P_(Q)(n) is the n^(th)element of the vector P_(Q) (equation (31)), P_(b) is the index of therelative center pilot subcarrier of each pilot cluster L_(p) (and thecenter pilot subcarrier of the first pilot cluster), and “:” indicatesall columns of the matrix F^(H) in the indicated rows. Note that thenumber of rows in each W^((j)) matrix is equal to the number N_(p)L_(PN)of pilot subcarriers in each transmitted OFDM signal.

A receive-antenna-dependent column vector y _(r) ^((s)) is given by thefollowing equation for −B_(p)≦a≦+B_(p):

y _(r) ^((s)) =y _(r) ^((s))(P _(p) ^(a))  (36)

where y_(r) ^((s)) is the signal received by the r^(th) receive antennaduring the symbol period s, and “(P_(p) ^(a))” (equation (28)), whichfor −B_(p)≦a≦+B_(p) equals [P_(p) ^(−Bp) . . . P_(p) ^(Bp)], indicateswhich elements of y_(r) ^((s)) form y _(r) ^((s)). For example, if thereare N_(p)=2 pilot clusters with L_(PN)=5 pilot subcarriers and three(B_(p)=1) non-guard pilot subcarriers located at subcarriers k=0(guard), k=1, k=2, k=3, k=4 (guard), and k=8 (guard), k=9, k=10, k=11,k=12 (guard), then for −1≦a≦+1 y _(r) ^((s)) would include the followingpilot subcarriers of y_(r) ^((s)) in the listed order: k=1, k=9, k=2,k=10, k=3, k=11.

A transmit-antenna- and path-dependent (but symbol-period-s independent)N_(p)×(2B_(p)+1) matrix q_(l) ^((i)H), which the first substage 158 maycalculate and/or store dynamically or ahead of time, is given by thefollowing equation:

q _(l) ^((i)H) =[f ^((iL+l)H) . . . f ^((iL+l)H)]  (37)

That is, q_(l) ^((i)H) has 2B_(p)+1 identical elements, and f^((iL+l))is a N_(p)×1 row vector. Examples of f^((iL)) and f^((iL+l)) aredescribed below in conjunction with FIG. 17. Using q_(l) ^((i)H) ofequation (37) and generating pilot patterns according to thepilot-pattern matrix p_(pat) ^((i)) of equation (54) allow the substages160 to be VSSO-Kalman-filter substages.

A transmit-antenna- and path-dependent (but symbol-period-s independent)matrix ø_(l) ^((i)), which the first substage 158 may determine and/orstore ahead of time, is (liven by the following equation:

$\begin{matrix}{\varnothing_{l}^{(i)} = {\begin{bmatrix}\theta_{l}^{(i)} & 0 & \ldots & 0 \\0 & \theta_{l}^{(i)} & \ldots & 0 \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & \theta_{l}^{(i)}\end{bmatrix}\begin{bmatrix}{W^{({- B_{p}})}B} \\\vdots \\{W^{({+ B_{p}})}B}\end{bmatrix}}} & (38)\end{matrix}$

A transmit-antenna- and path-dependent (but symbol-period-s independent)row vector q _(l) ^((i)H) (note the bar to distinguish this vector fromq_(l) ^((i)H) of equation (37)), which the first substage 158 maydetermine and/or store ahead of time, is given by the followingequation:

q _(l) ^((i)H)=[0_(1x(M−1)Q) q _(l) ^((i)H)ø_(l) ^((i))]  (39)

where 0_(1x(M−1)Q) is a row vector having (M−1)Q columns/elements thatare each equal to zero.

The observation scalar y _(r,l) ^((i,s)) for the engaged filter substage160 corresponding to the I^(th) path of the (r,i) channel is given bythe following equation:

y _(r,l) ^((i,s)) =q _(l) ^((i)H) y _(r) ^((s))  (40)

The measurement equation for the engaged filter substage 160corresponding to the I^(th) path of the (r,i) channel is given by thefollowing equation:

y _(r,l) ^((i,s)) = q _(l) ^((i)H) g _(r,l) ^((i,s)) + n _(r,l)^((i,s))  (41)

where n _(r,l) ^((i,s)) is the noise due to, e.g., interference on thepilot subcarriers of the (r,i) channel from the data subcarriers andAdditive White Gaussian Noise (AWGN) on this same channel. Although n_(r,l) ^((i,s)) may be unknown ahead of time, the first substage 158associated with the I^(th) path of the (r,i) channel may compute itsexpectation/variance σ _(r,l) ^(2(i))=E{| n _(r,l) ^((i,s))|²}dynamically or ahead of time by simulation or as a closed-formexpression in a conventional manner.

Referring to equation (40) and as further discussed below, themeasurement equation effectively relates the symbol recovered during thesymbol period s to the response of the (r,i) channel during s, and,referring to equation (41) and also as further discussed below, thestate equation (26), via the state vector g_(r,l) ^((i,s)), effectivelymodifies the result y _(r,l) ^((i,s)) given by the measurement equation(40) based on the response of the (r,i) channel during one or more priorsymbol periods. Furthermore, because y _(r,l) ^((i,s)) is a scalar, asdiscussed below, the filter substage 160 does not invert a matrix (atleast not in real time), which may significantly reduce the overallcomplexity of the channel estimator 138 as compared to a conventionalchannel estimator.

Still referring to FIG. 14, the operation of an embodiment of thechannel estimator 138 is described in terms of the second stage 152 ₀ ofthe partial channel-estimator portion 148, it being understood that theoperations of the other second stages 152 may be similar. Furthermore,in an embodiment, at least one path L₀ having a relative delay of zerois always present in the (r,i) channel, and the second stage 152 ₀ isdesigned to determine h_(r,l=0) ^((i,s)) for the I=L₀=0 path of the(r,i) channel having a relative delay of zero; therefore, in such anembodiment, the path monitor 154 always engages the second stage 152 ₀for the path I=0 of the (r,i) channel having a relatively delay of zero.Moreover, in the example below, the elements of h_(r,l) ^((i,s)) are fitto a straight line as described above.

First, the path monitor 154 determines the number Z and correspondingdelays of the paths L that compose the (r,i) channel, and engages, viathe switches 164, the second stages 152 that correspond to these paths.As discussed above, for purposes of the following example, it is assumedthat the path monitor 154 has engaged at least the second stage 152 ₀.

Next, the first stage 150 may determine and/or store quantities (atleast some of which are described above) that the second stage 152 ₀ mayneed for its calculations, to the extent that the first stage has notalready determined and/or stored these quantities. Furthermore, if someof these quantities (e.g. W^((j))) are independent of the transmitand/or receive antenna, then the first stage 150 of this or anotherchannel-estimator portion 148 may determine/store these quantities andprovide them to the other first stages to reduce or eliminate redundantprocessing as discussed above.

Similarly, the first substage 158 ₀ may determine and/or storequantities (at least some of which are described above) that the filtersubstage 160 ₀ may need for its calculations, to the extent that thefirst substage has not already determined and/or stored thesequantities. Furthermore, if some of these quantities are independent ofthe transmit and/or receive antenna, then the first substage 158 ₀ ofthis or another channel-estimation portion 148 may determine/store thesequantities and provide them to the other first substages to reduce oreliminate redundant processing as discussed above.

Next, the observation-scalar calculator 166 ₀ determines the observationscalar y _(r,l) ^((i,s)) for I=0 of the (r,i) channel according toequation (40).

Then, the state-vector predictor 168 ₀ determines the predicted statevector

_(r,l) ^((i,s)) for I=0 of the (r,i) channel according to the followingequation:

_(r,l) ^((i,s)) =Aĝ _(r,l) ^((i,s−1))  (42)

Where s=0 (the initial symbol period), the predictor 168 ₀ also providesan initial value for ĝ_(r,l) ^((i, −1)). This initial value may be zero,or it may be the expectation of ĝ_(r,l) ^((i, −1)). If the initial valueis the latter, then the predictor 168 ₀ may compute the expectation ofĝ_(r,l) ^((i, −1)) dynamically or ahead of time and store the computedexpectation. A technique for calculating the expectation of ĝ_(r,l)^((i, −1)) is described in S. M. Kay, “Fundamentals of StatisticalSignal Processing: Estimation Theory,” Prentice Hall: New Jersey (1993),which is incorporated by reference. After the initial symbol period s=0,the state-vector estimator 174 ₀ provides ĝ_(r,l) ^((i, s)), whichbecomes ĝ_(r,l) ^((i, s−1)) for the next symbol period s, as discussedbelow.

Next, the mean-square-error-matrix predictor 170 ₀ determines thepredicted mean-square-error matrix

_(r,l) ^((i,s)) for I=0 of the (r,i) path according to the followingequation:

_(r,l) ^((i,s)) =A{circumflex over (θ)} _(r,l) ^((i, s−1)) A ^(H) +G_(r,l) ^((i))  (43)

Where s=0 (the initial symbol period), the predictor 170 ₀ also providesan initial value for {circumflex over (θ)}_(r,l) ^((i, −1)). Thisinitial value may be zero, or it may be the expectation of the errorvariance in the state equation (26). If the initial value is the latter,then the predictor 170 ₀ may compute the expectation of the errorvariance in the state equation dynamically or ahead of time and storethe computed expectation. A technique for calculating the expectation ofthe error variance in the state equation (26) is described in S. M. Kay,“Fundamentals of Statistical Signal Processing: Estimation Theory,”Prentice Hall: New Jersey (1993), which is incorporated byreference._After the initial symbol period s=0, themean-square-error-matrix updater 176 ₀ provides {circumflex over(θ)}_(r,l) ^((i, s)), which becomes {circumflex over (θ)}_(r,l)^((i, s−1)) for the next symbol period s, as discussed below.

Then, the gain-vector calculator 172 ₀ determines a gain vector Ω_(r,l)^((i,s)) for I=0 of the (r,i) channel according to the followingequation:

$\begin{matrix}{\Omega_{r,l}^{({i,s})} = \frac{{\overset{\Cup}{\theta}}_{r,l}^{({i,s})}{\overset{\_}{q}}_{l}^{(i)}}{{\overset{\_}{\sigma}}_{r,l}^{2{({i,})}} + {{\overset{\_}{q}}_{l}^{{(i)}H}{\overset{\Cup}{\theta}}_{r,l}^{({i,s})}{\overset{\_}{q}}_{l}^{(i)}}}} & (44)\end{matrix}$

Next, the state-vector estimator 174 ₀ generates the estimated statevector ĝ_(r,l) ^((i,s)) for I=0 of the (r,i) channel according to thefollowing equation:

ĝ _(r,l) ^((i,s))=

_(r,l) ^((i,s))+Ω_(r,l) ^((i,s)) [ y _(r,l) ^((i,s)) − q _(l) ^((i)H)

_(r,l) ^((i,s))]  (45)

As discussed above, ĝ_(r,l) ^((i,s)) is fed back to the state-vectorpredictor 168 ₀ to be used in equation (42) as ĝ_(r,l) ^((i, s−1)) forthe next symbol period.

Then, the mean-square-error-matrix updater 176 ₀ generates an updatedmean-square-error matrix {circumflex over (θ)}_(r,l) ^((i,s)) for I=0 ofthe (r,i) channel according to the following equation:

{circumflex over (θ)}_(r,l) ^((i,s)) =[I _(MQ)−Ω_(r,l) ^((i,s)) q _(l)^((i)H)]

_(r,l) ^((i,s))  (46)

where I_(MQ) is an identity matrix of dimensions M(row)×Q(column) and“−” is a minus sign. Furthermore, as discussed above, {circumflex over(θ)}_(r,l) ^((i,s)) is fed back to the mean-square-error-matrixpredictor 170 ₀ to be used in equation (43) as {circumflex over(θ)}_(r,l) ^((i, s−1)) for the next symbol period.

Next, the scaling-vector calculator 178 ₀ determines the scaling vectorh _(r,l) ^((i,s)) for I=0 of the (r,i) channel for a straight-lineapproximation of the elements of h_(r,l) ^((i,s)) according to one ofthe two following equations:

h _(r,l) ^((i,s)) =ĝ _(r,l) ^((i,s))(MQ−Q:MQ−1)  (47)

h _(r,l) ^((i, s−M)) =ĝ _(r,l) ^((i,s))(0:Q−1)  (48)

Equation (47) may be referred to as the normal Kalman filter (NKF)output, and equation (48) may be referred to as the Kalman fixed-lagsmoother (KFLS) output, which is effectively a low-pass filtered output.Generally, the KFLS output is more accurate, but has a higher latency,than the NKF output.

Then, the third stage path-vector calculator 162 ₀ determines the pathvector h_(r,l) ^((i,s)) for I=0 of the (r,i) channel according toequation (24) using either h _(r,l) ^((i,s)) from equation (47) or h_(r,l) ^((i, s−M)) from equation (48).

As stated above, the other engaged second stages 152 of thechannel-estimator portion 148 may operate in a similar manner togenerate h _(r,l) ^((i,s)) and h_(r,l) ^((i,s)) for the paths I of the(r,i) channel to which they correspond. Typically, all engaged secondstages 152 generate h _(r,l) ^((i,s)) according to equation (47) orequation (48) for a symbol period s, although it is contemplated thatsome second stages may generate h _(r,l) ^((i,s)) according to equation(47) while other second stages may generate h _(r,l) ^((i,s)) accordingto equation (48) for a same symbol period s.

Next, the third stage partial channel-matrix calculator 156 generates anintermediate partial-channel-estimation matrix H _(r) ^((i,s)) from thepath-response vectors h_(r,l) ^((i,s)) for all of the paths 0≦I≦Z−1 thatcompose the (r,i) channel according to the following equation:

Ĥ _(r) ^((i,s))(m,n)=ĥ _(r,<m−n>) ^((i,s))( s+m),for 0≦m≦N−1 and0≦n≦N−1  (49)

Then, the third stage partial-channel-matrix calculator 156 generatesthe partial-channel-estimation matrix Ĥ_(r) ^((i,s)) for the (r,i)channel according to the following equation:

$\begin{matrix}{{\hat{H}}_{r}^{({i,s})} = {\frac{1}{N}F\; {\underset{\_}{\hat{H}}}_{r}^{({i,s})}F^{H}}} & (50)\end{matrix}$

Still referring to FIG. 14, alternate embodiments of the channelestimator 138 and the partial channel-estimator portion 148 arecontemplated. For example, alternate embodiments described above inconjunction with the channel estimator 36 of FIGS. 9 and 10 may beapplicable to the channel estimator 138. Furthermore, the functionscontributed to any of the components of the channel estimator 138 may beperformed in hardware, software, or a combination of hardware andsoftware, where the software is executed by a controller such as aprocessor. Moreover, although described as VSSO Kalman filters, one ormore of the second substages 160 may be another type of recursivefilter, for example, another type of recursive filter that does notinvert a matrix, at least not in real time. In addition, althoughdescribed as operating in response to APPC pilot clusters (FIG. 9), thechannel estimator 138 may be modified (e.g., by modifying some or all ofthe above equations described in relation to FIGS. 11-14 according toknown principles) to operate in response to FDKD pilot clusters (FIG. 8)or other types of pilot clusters. Furthermore, instead of, or inaddition to, disengaging the unused second stages 152, the path monitor154 may cause these unused second stages to enter a low- or no-powermode to save power.

FIG. 15 is a diagram of an embodiment of apartial-channel-estimation-matrices combiner 190 of the channelestimator 138 of FIG. 13.

The combiner 190 generates the RN×TN channel-estimation matrix Ĥ^((s))from the RT N×N partial channel-estimation matrices Ĥ_(r) ^((i,s)) (for0≦i≦T−1 and 0≦r≦R−1) according to the following equation:

Ĥ ^((s)) =[Ĥ _(r=0) ^((i=0,s)) Ĥ _(r=0) ^((i=1,s)) . . . Ĥ _(r=0)^((i=T−1,s))); (Ĥ _(r=1) ^((i=0,s)) Ĥ _(r=1) ^((i=1,s)) . . . Ĥ _(r=1)^((i=T−1,s))); . . . ; (Ĥ _(r=R−1) ^((i=0,s)) Ĥ _(r=R−1) ^((i=1,s)) . .. Ĥ _(r=R−1) ^((i=T−1,s)))]^(T)  (51)

such that one may think of Ĥ^((s)) as a matrix that includes R T×Nmatrices stacked atop one another—note that the matrices withinparenthesis (e.g., Ĥ_(r=0) ^((i=0,s))Ĥ_(r=0) ^((i=1,s)) . . . Ĥ_(r=0)^((i=T−1,s))) are not multiplied together, but are positioned next toone another.

FIG. 16 is a diagram of an embodiment of a received-signal combiner 136of the receiver 130 of FIG. 13. The combiner 130 generates the RN×1received-signal vector y^((s)) from the R N×1 partial received-signalcolumn vectors y_(r) ^((s)) (0≦r≦R−1) according to the followingequation:

y ^((s)) =[y _(r=0) ^((s)T) y _(r=1) ^((s)T) . . . y _(r=R−1)^((s)T)]^(T)  (52)

such that one may think of y^((s)) as a vector that includes 1 column ofR N×1 vectors.

FIG. 17 is a diagram of an embodiment of a MIMO-OFDM transmitter 200,which may generate a pilot-symbol pattern p_(pat) ^((i)) (for 0≦i≦T−1)that is compatible with a receiver such as the receiver 130 of FIG. 13.

The transmitter 200 includes T transmit paths 202 ₀-202 _(T−1). Forbrevity, only the path 202 ₀ is described in detail, it being understoodthat the remaining paths 202 ₁-202 _(T−1) may be similar.

The transmit path 202 ₀ includes a pilot generator 204 ₀, a datagenerator 206 ₀, a pilot-subcarrier-coefficient generator 208 ₀, adata-subcarrier-coefficient generator 210 ₀, an Inverse FourierTransform (IFFT) unit 212 ₀, a digital-to-analog converter (DAC) 214 ₀,a modulator 216 ₀, and an antenna 218 ₀.

The pilot generator 204 ₀ generates pilot subsymbols from pilotinformation that may include a pilot pattern in the form of apilot-pattern matrix p_(pat) ^((i)), which is discussed further below.

Similarly, the data generator 206 ₀ generates data subsymbols from datainformation.

The pilot-subcarrier-coefficient generator 208 ₀ generates from eachpilot subsymbol a respective complex frequency-domain coefficient formapping to the respective pilot subcarrier.

Similarly, the data-subcarrier-coefficient generator 210 ₀ generatesfrom each data subsymbol a respective complex frequency-domaincoefficient for mapping to the respective data subcarrier.

The IFFT unit 212 ₀ transforms the pilot-subcarrier and data-subcarriercoefficients into a digital time-domain waveform.

The DAC 214 ₀ converts the digital time-domain waveform into an analogtime-domain waveform.

The modulator 216 ₀ modulates a carrier signal (e.g., a 5.4 GHz carrier)with the analog waveform.

And the antenna 218 ₀ transmits the modulated carrier signal forreception by a receiver such as the receiver 130 of FIG. 13. The antenna218 ₀ may also function as a receive antenna if the transmitter 200 ispart of a transmitter/receiver device.

In an embodiment, the pilot generators 204 may each generate arespective pilot pattern according to a respective pilot-pattern matrixp_(pat) ^((i)) such that each column of p_(pat) ^((i)) generated by oneof the pilot generators is orthogonal to every column of all the otherpilot-pattern matrices p_(pat) ^((i)) generated by the other pilotgenerators. Such orthogonality is present when the following equation istrue:

p _(pat) ^((m)) p _(pat) ^((n)H)=0 for 0≦m≦T−1,0≦n≦T−1,and m≠n  (53)

An example of such orthogonal pilot-pattern matrices is given by thefollowing equation:

p _(pat) ^((i)) =[f ^((iZ)) ; f ^((iZ)) ; . . . ; f ^((iZ))] for0≦i≦T−1  (54)

where i is the transmit-antenna index, Z is the number of paths L ineach channel (in an embodiment it is assumed that each channel alwayshas the same number Z of paths L), and p_(pat) ^((i)) has N_(p) rows(each row represents a pilot cluster) and L_(PN)=2w_(p)+1 identicalcolumns (i.e., f^((iZ)) f^((iZ)H)=1).

An example of the N_(p)×1 column vector f^((iZ)) is given by thefollowing equation:

f ^((iZ))=[1e ^(−j2πΔf) ^(p) ^(iZ) e ^(−j2π2Δf) ^(p) ^(iZ) e ^(−j2π3Δf)^(p) ^(iZ) . . . e ^(−j2π(N) ^(p) ^(−1)Δf) ^(p) ^(iZ)]  (55)

where

${\Delta \; f_{p}} = {\frac{1}{N_{p}}.}$

It has been found that such orthogonal pilot-pattern matrices p_(pat)^((i)) allow a MIMO-OFDM channel estimator, such as the channelestimator 138 of FIG. 13, to avoid performing a matrix inversion (atleast in real time) by including, e.g., recursive filters such as theVSSO Kalman filter substages 160 of FIG. 14.

In another embodiment, the pilot generators 204 may each generate arespective pilot pattern according to a respective pilot-pattern matrixp_(pat) ^((i)) such that not only is each column of p_(pat) ^((i))generated by one of the pilot generators orthogonal to every column ofthe pilot-pattern matrices p_(pat) ^((i)) generated by the other pilotgenerators, but each column of p_(pat) ^((i)) is also orthogonal toevery other column of the same matrix p_(pat) ^((i)). Such “dual”orthogonality is present when the following equations are true:

p _(pat) ^((m)) p _(pat) ^((n)H)=0 for 0≦m≦T−1,0≦n≦T−1,and m≠n  (53)

f _(pat) ^((d)) f _(pat) ^((v)H)=0 for 0≦d≦L _(PN)−1,0≦v≦L _(PN)−1,andd≠v  (54)

where f_(pat) ^((i,u)) are the L_(PN) column vectors that composep_(pat) ^((i)).

An example of such pilot-pattern matrices with dual orthogonality isgiven by the following equation:

p _(pat) ^((i)) =[f ^((iL) ^(p) ^(Z+0Z)) ; f ^((iL) ^(p) ^(Z+1Z)) ; f^((iL) ^(p) ^(Z+2Z)) ; . . . ; f ^((iL) ^(p) ^(Z+(L) ^(p) ^(−1)Z)] for0≦i≦T−1  (55)

where i is the transmit-antenna index, Z is the number of paths L ineach channel (in an embodiment it is assumed that each channel alwayshas the same number Z of paths L), and p_(pat) ^((i)) has N_(p) rows(each row represents a pilot cluster) and L_(PN)=2w_(p)+1 orthogonalcolumns such that f^((iL) ^(p) ^(Z+d))f^((iL) ^(p) ^(Z+v)H)=0 for0≦d≦(L_(PN)−1)Z, 0≦v≦(L_(PN)−1)Z, and d≠v.

An example of the N_(p)×1 column vectors f^((iL) ^(p) ^(Z+u)) for0≦u≦(L_(p)−1)Z is given by the following equation:

f ^((iL) ^(p) ^(Z+u))=[1e ^(−j2πΔf) ^(p) ^((iL) ^(p) ^(Z+u)) e^(−j2π2Δf) ^(p) ^((iL) ^(p) ^(Z+u)) e ^(−j2π3Δf) ^(p) ^((iL) ^(p)^(Z+u)) . . . e ^(−j2π(N) ^(p) ^(−1)Δf) ^(p) ^((iL) ^(p) ^(Z+u))]  (56)

where

${\Delta \; f_{p}} = {\frac{1}{N_{p}}.}$

It has been found that such dual-orthogonal pilot-pattern matricesp_(pat) ^((i)) may improve the performance of a MIMO-OFDM channelestimator that does not include recursive filters such as the VSSOKalman filter substages 160 of FIG. 14. Furthermore, suchdual-orthogonal pilot-pattern matrices p_(pat) ^((i)) may also be usablewith a MIMO-OFDM channel estimator, such as the channel estimator 138 ofFIG. 13, that includes recursive filters such as the VSSO Kalman filtersubstages 160 of FIG. 14.

Still referring to FIG. 17, alternate embodiments of the transmitter 200are contemplated. For example, the modulators 216 may be omitted.Furthermore, the functions performed any of the components of thetransmitter 200 may be performed in hardware, software, or a combinationof hardware and software, where the software is executed by a controllersuch as a processor. Moreover, pilot patterns and pilot-pattern matricesother than those described are contemplated.

From the foregoing it will be appreciated that, although specificembodiments have been described herein for purposes of illustration,various modifications may be made without deviating from the spirit andscope of the disclosure. Furthermore, where an alternative is disclosedfor a particular embodiment, this alternative may also apply to otherembodiments even if not specifically stated. Moreover, the componentsdescribed above may be disposed on a single or multiple IC dies to formone or more ICs, these one or more ICs may be coupled to one or moreother ICs to form a device such as a transceiver, and one or more ofsuch devices may be coupled or otherwise used together to form a system.

1. A channel estimator, comprising: a first stage configurable togenerate a first observation scalar for a first communication path of afirst communication channel; a second stage configurable to generate asecond observation scalar for a first communication path of a secondcommunication channel; and a third stage configurable to generatechannel estimation coefficients in response to the first and secondobservation scalars.
 2. The channel estimator of claim 1 wherein: thefirst stage is configurable: to receive a first signal having a firstpilot subcarrier; and to generate the first observation scalar inresponse to first information carried by the first pilot subcarrier; andthe second stage is configurable: to receive a second signal having asecond pilot subcarrier; and to generate the second observation scalarin response to second information carried by the second pilotsubcarrier.
 3. The channel estimator of claim 1 wherein the channelestimation coefficients include a multi dimensional array offrequency-domain channel estimation coefficients for the first andsecond communication channels.
 4. The channel estimator of claim 1,further including: a fourth stage configurable to generate a thirdobservation scalar for a second communication path of the firstcommunication channel; a fifth stage configurable to generate a fourthobservation scalar for a second communication path of the secondcommunication channel; and wherein the second stage is configurable togenerate the channel estimation coefficients in response to the thirdand fourth observation scalars.
 5. The channel estimator of claim 1,further comprising: a fourth stage configurable to generate first pathestimation coefficients for the first communication path of the firstcommunication channel in response to the first observation scalar; afifth stage configurable to generate second path estimation coefficientsfor the first communication path of the second communication channel inresponse to the second observation scalar; and wherein the third stageis configurable to generate the channel-estimation coefficients inresponse to the first and second path-estimation coefficients.
 6. Thechannel estimator of claim 5 wherein: the first and second pathestimation coefficients each comprise time domain coefficients; and thechannel estimation coefficients comprise frequency domain coefficients.7. The channel estimator of claim 1, further including: a fourth stageconfigurable to generate a third observation scalar for a secondcommunication path of the first communication channel; a fifth stageconfigurable to generate a fourth observation scalar for a secondcommunication path of the second communication channel; a sixth stageconfigurable to generate first path estimation coefficients in responseto the first observation scalar; a seventh stage configurable togenerate second path estimation coefficients in response to the secondobservation scalar; an eighth stage configurable to generate third pathestimation coefficients in response to the third observation scalar; aninth stage configurable to generate fourth path estimation coefficientsin response to the fourth observation scalar; and wherein the thirdstage is configurable to generate the channel estimation coefficients inresponse to the first, second, third, and fourth path estimationcoefficients.
 8. The channel estimator of claim 1, further including: afirst Kalman filter configurable to generate in response to the firstobservation scalar first intermediate coefficients; a second Kalmanfilter configurable to generate in response to the second observationscalar second intermediate coefficients; a fourth stage configurable togenerate first path estimation coefficients in response to the firstintermediate coefficients; a fifth stage configurable to generate secondpath estimation coefficients in response to the second intermediatecoefficients; and wherein the third stage is configurable to generatethe channel estimation coefficients in response to the first and secondintermediate coefficients.
 9. The channel estimator of claim 1, furtherincluding: a first Kalman filter configurable to generate in response tothe first observation scalar first intermediate coefficients; a fourthstage configurable to generate first path estimation coefficients inresponse to the first intermediate coefficients; a second Kalman filterconfigurable to generate in response to the second observation scalarsecond intermediate coefficients; a fifth stage configurable to generatesecond path estimation coefficients in response to the secondintermediate coefficients; a sixth stage configurable to generate athird observation scalar for a second communication path of the firstcommunication channel; a third Kalman filter configurable to generate inresponse to the third observation scalar third intermediatecoefficients; a seventh stage configurable to generate third pathestimation coefficients in response to the third intermediatecoefficients; an eighth stage configurable to generate a fourthobservation scalar for a second communication path of the secondcommunication channel; a fourth Kalman filter configurable to generatein response to the fourth observation scalar fourth intermediatecoefficients; a ninth stage configurable to generate fourth pathestimation coefficients in response to the fourth intermediatecoefficients; and wherein the third stage is configurable to generatethe channel estimation coefficients in response to the first, second,third, and fourth path estimation coefficients.
 10. A receiver,comprising: a channel estimator, including: a first stage configurableto generate a first observation scalar for a communication path of afirst communication channel; a second stage configurable to generate asecond observation scalar for a communication path of a secondcommunication channel; and a third stage configurable to generatechannel estimation coefficients in response to the first and secondobservation scalar.
 11. The receiver of claim 10, further comprising: anantenna configurable to receive a first orthogonal frequency divisionmultiplexed signal over the first communication channel and a secondorthogonal frequency division multiplexed signal over the secondcommunication channel; wherein the first stage of the channel estimatoris configurable to generate the first observation scalar in response tothe first received signal; and wherein the second stage of the channelestimator is configurable to generate the second observation scalar inresponse to the second received signal.
 12. The receiver of claim 10,further comprising: a first antenna configurable to receive a firstorthogonal frequency division multiplexed signal over the firstcommunication channel; a second antenna configurable to receive a secondorthogonal frequency division multiplexed signal over the secondcommunication channel; wherein the first stage of the channel estimatoris configurable to generate the first observation scalar in response tothe first received signal; and wherein the second stage of the channelestimator is configurable to generate the second observation scalar inresponse to the second received signal.
 13. The receiver of claim 10,further comprising: a transform unit configurable to convert a firstorthogonal frequency division multiplexed signal from the firstcommunication channel into first frequency domain coefficients and toconvert a second orthogonal frequency division multiplexed signal fromthe second communication channel into second frequency domaincoefficients; wherein the first stage of the channel estimator isconfigurable to generate the first observation scalar in response to thefirst frequency domain coefficients; and wherein the second stage of thechannel estimator is configurable to generate the second observationscalar in response to the second frequency domain coefficients.
 14. Thereceiver of claim 10, further comprising a data recovery unitconfigurable to recover data carried by first and second orthogonalfrequency divisional multiplexed signals from the first and secondcommunication channels, respectively, in response to the channelestimation coefficients.
 15. The receiver of claim 10, furthercomprising: a data recovery unit configurable to recover coded datacarried by first and second orthogonal frequency division multiplexedsignals from the first and second communication channels, respectively,in response to the channel estimation coefficients; and a decoderoperable to decode the recovered coded data.
 16. The receiver of claim10, further comprising a controller configurable to control at least onefunction of the channel estimator.
 17. The receiver of claim 10, furthercomprising a controller configurable to implement the channel estimator.18. A communication unit, comprising: a receiver configurable to receivea first orthogonal frequency division multiplexed signal from a firstcommunication channel having a communication path and a secondorthogonal frequency division multiplexed signal from a secondcommunication channel having a communication path, the receiverincluding: a channel estimator, including: a first stage configurable togenerate from the first signal a first observation scalar for thecommunication path of the first communication channel; a second stageconfigurable to generate from the second signal a second observationscalar for the communication path of the second communication channel;and a third stage configurable to generate channel estimationcoefficients in response to the first and second observation scalars;and a transmitter configurable to transmit third and fourth orthogonalfrequency division multiplexed signals.
 19. The communication unit ofclaim 18, further comprising: a first antenna configurable: to providethe first signal to the receiver; and to receive the third signal fromthe transmitter; and a second antenna configurable: to provide thesecond signal to the receiver; and to receive the fourth signal from thetransmitter.
 20. A system, comprising: a first communication unit,including: a first receiver configurable to receive a first orthogonalfrequency division multiplexed signal from a first communication channelhaving a communication path and a second orthogonal frequency divisionmultiplexed signal from a second communication channel having acommunication path, the receiver including: a channel estimator,including: a first stage configurable to generate from the first signala first observation scalar for the communication path of the firstcommunication channel; a second stage configurable to generate from thesecond signal a second observation scalar for the communication path ofthe second communication channel; and a third stage configurable togenerate channel estimation coefficients in response to the first andsecond observation scalars; and a first transmitter configurable totransmit third and fourth orthogonal frequency division multiplexedsignals; and a second communication unit, including: a second receiverconfigurable to receive the third and fourth signals from the firsttransmitter; and a second transmitter configurable to transmit the firstand second signals to the first receiver.
 21. A computer-readable mediumstoring instructions that when executed by a computing apparatus causethe apparatus: to generate a first observation scalar for acommunication path of a first communication channel; to generate asecond observation scalar for a communication path of a secondcommunication channel; and to generate channel estimation coefficientsin response to the first and second observation scalars.
 22. A method,comprising: receiving a first signal over a first communication channelhaving a number of communication paths; receiving a second signal over asecond communication channel having a number of communication paths;generating in response to the first signal a first observation scalarfor a first one of the communication paths of the first channel;generating in response to the second signal a second observation scalarof a first one of the communication paths of the second channel; andestimating channel coefficients in response to the first and secondobservation scalars.
 23. The method of claim 22 wherein receiving thefirst and second signals comprises receiving first and secondorthogonal-frequency-division-multiplexed signals that are experiencingDoppler spread.
 24. The method of claim 22 wherein receiving the firstand second signals comprises receiving the signals at a destination thatis moving relative to a source of the signals.
 25. The method of claim22 wherein receiving the signals comprises receiving the signals from asource that is moving relative to a destination at which the signals arebeing received.
 26. The method of claim 22 wherein: the number ofcommunication paths of the first communication channel equals one; andthe number of communication paths of the second communication channelequals one.
 27. The method of claim 22 wherein: the number ofcommunication paths of the first communication channel is greater thanone; and the number of communication paths of the second communicationchannel is greater than one.
 28. The method of claim 22 wherein:receiving the first signal comprises receive a number of pilotsubcarriers of the first signal; generating the first observation scalarcomprises generating the first observation scalar in response toinformation carried by the number of pilot subcarriers of the firstsignal; receiving the second signal comprises receive a number of pilotsubcarriers of the second signal; and generating the second observationscalar comprises generating the second observation scalar in response toinformation carried by the number of pilot subcarriers of the secondsignal.
 29. The method of claim 21, further comprising: generating inresponse to the first signal a third observation scalar for a second oneof the communication paths of the first channel; generating in responseto the second signal a fourth observation scalar for a second one of thecommunication paths of the second channel; and estimating the channelcoefficients in response to the third and fourth observation scalars.30. The method of claim 22 wherein estimating the channel coefficientscomprises: estimating first path coefficients for the first path of thefirst communication channel in response to the first observation scalar;estimating second path coefficients for the first path of the secondcommunication channel in response to the second observation scalar; andestimating the channel coefficients in response to the first and secondpath coefficients.
 31. The method of claim 22 wherein estimating thechannel coefficients comprises estimating the channel coefficients inresponse to a Kalman algorithm that is responsive to the first andsecond observation scalars.